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    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
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    <link:label id="lab_us-gaap_NoncashMergerRelatedCosts_ba87e72e-3890-493e-be27-9869d9701aac_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashMergerRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Merger-related and restructuring expenses</link:label>
    <link:label id="lab_us-gaap_NoncashMergerRelatedCosts_label_en-US" xlink:label="lab_us-gaap_NoncashMergerRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Merger Related Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashMergerRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncashMergerRelatedCosts"/>
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    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_017c7696-3f8d-4755-9a81-02729325f0f9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of long-term borrowed funds</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RepaymentsOfLongTermDebt"/>
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    <link:label id="lab_us-gaap_CollateralDomain_4c4853fe-4d35-41b6-a382-ce2ba89d7700_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral [Domain]</link:label>
    <link:label id="lab_us-gaap_CollateralDomain_label_en-US" xlink:label="lab_us-gaap_CollateralDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Held [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CollateralDomain"/>
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    <link:label id="lab_dei_CoverAbstract_f8136faa-0273-461c-b761-40faf0717fa2_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CoverAbstract"/>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_b29bf20d-e688-4e47-883f-99930bfd686a_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase in cash, cash equivalents, and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLoansHeldForSale_dbe7ab42-44f0-4bcf-b760-a1ea2c335d34_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for sale</link:label>
    <link:label id="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLoansHeldForSale_label_en-US" xlink:label="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Loans Held For Sale</link:label>
    <link:label id="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLoansHeldForSale_documentation_en-US" xlink:label="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Loans Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLoansHeldForSale" xlink:href="fbc-20240630.xsd#fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLoansHeldForSale"/>
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    <link:label id="lab_us-gaap_GainLossOnSalesOfLoansNet_a683543b-366d-4fc2-bba1-60b2c2293f97_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gain on loan sales and securitizations</link:label>
    <link:label id="lab_us-gaap_GainLossOnSalesOfLoansNet_label_en-US" xlink:label="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sales of Loans, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSalesOfLoansNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainLossOnSalesOfLoansNet"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_2de0c98d-0880-485c-b1c6-3ab37f0eb547_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Minimum Contractual Lease Obligations</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
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    <link:label id="lab_fbc_RealPropertyCollateralMember_f4628a35-6dc5-424b-a383-bbac48064065_terseLabel_en-US" xlink:label="lab_fbc_RealPropertyCollateralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Property</link:label>
    <link:label id="lab_fbc_RealPropertyCollateralMember_label_en-US" xlink:label="lab_fbc_RealPropertyCollateralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Property Collateral [Member]</link:label>
    <link:label id="lab_fbc_RealPropertyCollateralMember_documentation_en-US" xlink:label="lab_fbc_RealPropertyCollateralMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Property Collateral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_RealPropertyCollateralMember" xlink:href="fbc-20240630.xsd#fbc_RealPropertyCollateralMember"/>
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    <link:label id="lab_dei_TradingSymbol_415ed8ed-cb28-407b-8e5a-a63a68288ff7_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_TradingSymbol"/>
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    <link:label id="lab_us-gaap_FairValueHedgingMember_4a2ea541-1c1f-44a0-b81e-b2b84a6d9355_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value hedging</link:label>
    <link:label id="lab_us-gaap_FairValueHedgingMember_label_en-US" xlink:label="lab_us-gaap_FairValueHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hedging [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueHedgingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueHedgingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueHedgingMember" xlink:to="lab_us-gaap_FairValueHedgingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgedStatusDomain_6c5108ee-4ec4-4482-9037-6f6cdf845f88_terseLabel_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:label id="lab_us-gaap_PledgedStatusDomain_label_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgedStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgedStatusDomain" xlink:to="lab_us-gaap_PledgedStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_46cc65cd-59cc-4723-b78b-f1f7c8238de5_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_4e9d5718-97bc-47a1-b87c-10ef2a45a127_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amount</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset</link:label>
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    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonNeosMember"/>
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    <link:label id="lab_fbc_InterestRateSwapsandSwaptionsMember_3176ccef-0ad0-412f-9a9d-bfb7e8633de1_verboseLabel_en-US" xlink:label="lab_fbc_InterestRateSwapsandSwaptionsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaps and swaptions</link:label>
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    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_faf49e8f-908e-4404-a0e7-8113925b423c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfFinancingReceivablesPastDueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_4bc5858e-0d43-48e6-b967-3330b1716b16_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at fair value measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_7044e3ec-d656-45e3-94ab-54cae21a99a2_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseNet" xlink:to="lab_us-gaap_InterestIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember_46c31baf-d5b1-40ba-96b7-0ef96241aa6f_terseLabel_en-US" xlink:label="lab_fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaps on multi-family loans held for investment</link:label>
    <link:label id="lab_fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember_label_en-US" xlink:label="lab_fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap On Multi-Family Loans Held For Investment [Member]</link:label>
    <link:label id="lab_fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember_documentation_en-US" xlink:label="lab_fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap On Multi-Family Loans Held For Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember" xlink:href="fbc-20240630.xsd#fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember" xlink:to="lab_fbc_InterestRateSwapOnMultiFamilyLoansHeldForInvestmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_b6036621-1623-46b2-8cb6-18e45ea5fc79_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Potential dilutive common shares (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted, Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:to="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransferToOtherRealEstate_2a0fbceb-918c-4822-b9ec-22f651f16aee_terseLabel_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers to repossessed assets from loans</link:label>
    <link:label id="lab_us-gaap_TransferToOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Transfer to Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferToOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransferToOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransferToOtherRealEstate" xlink:to="lab_us-gaap_TransferToOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_057da22e-1029-4c40-b282-4b69d4d49a1e_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncumulative convertible preferred stock (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquitySharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesIssued" xlink:to="lab_us-gaap_TemporaryEquitySharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAbstract" xlink:to="lab_us-gaap_LeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgedStatusAxis_171b2744-3f6a-4398-87bc-50c66b4bfb2d_terseLabel_en-US" xlink:label="lab_us-gaap_PledgedStatusAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged Status [Axis]</link:label>
    <link:label id="lab_us-gaap_PledgedStatusAxis_label_en-US" xlink:label="lab_us-gaap_PledgedStatusAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledged Status [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgedStatusAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgedStatusAxis" xlink:to="lab_us-gaap_PledgedStatusAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_ddd947d0-8a89-4136-9d62-24c3eb6a7e61_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior year</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Originated, More than Five Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OtherLoansMember_f27d3696-d791-46dd-ba99-40163fc8b967_terseLabel_en-US" xlink:label="lab_fbc_OtherLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_fbc_OtherLoansMember_label_en-US" xlink:label="lab_fbc_OtherLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Loans [Member]</link:label>
    <link:label id="lab_fbc_OtherLoansMember_documentation_en-US" xlink:label="lab_fbc_OtherLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OtherLoansMember" xlink:href="fbc-20240630.xsd#fbc_OtherLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OtherLoansMember" xlink:to="lab_fbc_OtherLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_0ac43e6f-30e6-410b-a091-ebb2dc1f3b58_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VariableInterestEntityDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:to="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateBondSecuritiesMember_e34d05b3-d986-4283-8f6e-2d3a3d2abc66_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate bonds</link:label>
    <link:label id="lab_us-gaap_CorporateBondSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_CorporateBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Bond Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateBondSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CorporateBondSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateBondSecuritiesMember" xlink:to="lab_us-gaap_CorporateBondSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_3ecf1141-64d3-4a44-adf8-6d27512cc67f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_df36e80b-26c8-4dbf-ae84-00fc18b813f6_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_629f0db0-0c3b-4eb7-859c-e1c2f96aa41b_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CASH FLOWS FROM OPERATING ACTIVITIES:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionIntangibleAssetsAcquired1_361d4309-3381-4526-a596-fccfcb6a6623_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionIntangibleAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Intangible Assets Acquired</link:label>
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    <link:label id="lab_us-gaap_RepurchaseAgreementsMember_7942fa76-5e7e-458c-a3a3-7cfbc5691cf6_terseLabel_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_us-gaap_RepurchaseAgreementsMember_label_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepurchaseAgreementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RepurchaseAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepurchaseAgreementsMember" xlink:to="lab_us-gaap_RepurchaseAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost_e166910c-b8e9-472c-8fa5-8f078c38f10b_totalLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net periodic (credit) expense</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Net Periodic Benefit Cost (Credit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:to="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfLiabilitiesAssumed1_5b0a88b9-d6ff-48d8-8af4-5f652c867f86_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfLiabilitiesAssumed1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities assumed</link:label>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfLiabilitiesAssumed1_label_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfLiabilitiesAssumed1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Value of Liabilities Assumed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashOrPartNoncashAcquisitionValueOfLiabilitiesAssumed1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncashOrPartNoncashAcquisitionValueOfLiabilitiesAssumed1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashOrPartNoncashAcquisitionValueOfLiabilitiesAssumed1" xlink:to="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfLiabilitiesAssumed1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_2dfff816-79b9-4960-9b0d-a6122711d734_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_a4ca5543-f541-4182-8572-5f84f52d2d66_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember_c6b2a2cd-1652-4059-ba9b-96130fa05837_terseLabel_en-US" xlink:label="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">US States and Political Subdivisions Debt Securities</link:label>
    <link:label id="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember_label_en-US" xlink:label="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US States and Political Subdivisions Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_USStatesAndPoliticalSubdivisionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:to="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementAdjustmentMember_2f0f5859-10c2-45de-a1cc-27f96b9b253c_terseLabel_en-US" xlink:label="lab_srt_RestatementAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Adjustment</link:label>
    <link:label id="lab_srt_RestatementAdjustmentMember_label_en-US" xlink:label="lab_srt_RestatementAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period, Adjustment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementAdjustmentMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RestatementAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementAdjustmentMember" xlink:to="lab_srt_RestatementAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_c4cb6321-91f6-423a-ba4a-373c2dc2a51a_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FlagstarStatutoryTrustVIMember_19b1180e-a873-40c9-bde1-7c30693997ef_terseLabel_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust VI</link:label>
    <link:label id="lab_fbc_FlagstarStatutoryTrustVIMember_label_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust VI [Member]</link:label>
    <link:label id="lab_fbc_FlagstarStatutoryTrustVIMember_documentation_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust VI</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FlagstarStatutoryTrustVIMember" xlink:href="fbc-20240630.xsd#fbc_FlagstarStatutoryTrustVIMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FlagstarStatutoryTrustVIMember" xlink:to="lab_fbc_FlagstarStatutoryTrustVIMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoan_3ab0f032-c087-4c3f-bd70-8cc174d7fe1a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Loans Converted to Term Loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoan_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Revolving, Converted to Term Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoan" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoan" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoan" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent_52b911d0-2aca-4e3a-ae13-1e23dd616147_terseLabel_en-US" xlink:label="lab_fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excluding loans with government guarantees and warehouse loans, the allowance for credit losses</link:label>
    <link:label id="lab_fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent_label_en-US" xlink:label="lab_fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Unguaranteed, Allowance For Credit Loss To Outstanding, Percent</link:label>
    <link:label id="lab_fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent_documentation_en-US" xlink:label="lab_fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Unguaranteed, Allowance For Credit Loss To Outstanding, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent" xlink:href="fbc-20240630.xsd#fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent" xlink:to="lab_fbc_FinancingReceivableUnguaranteedAllowanceForCreditLossToOutstandingPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_85e121b4-fbaf-4161-8f06-6b26a1452d7b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromOneToTwoYearsOfBalanceSheetDate_a8459774-2e1a-4548-865f-4b942d4a862b_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromOneToTwoYearsOfBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_9ccf0bfc-7c4d-4d8d-88ac-b5371ced7acf_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total comprehensive (loss) income, net of tax</link:label>
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    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_e8078604-6bb7-42a6-991f-51215be58181_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Quantitative Disclosures</link:label>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Quantitative Disclosures [Line Items]</link:label>
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    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_514c0759-f727-4d67-88a7-ac8ec386e023_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on common stock (in dollars per share)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockDividendsPerShareCashPaid"/>
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    <link:label id="lab_us-gaap_MortgageBackedSecuritiesOtherMember_352603ed-8cac-40f4-9de6-754867c9c9af_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage-backed securities forwards</link:label>
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    <link:label id="lab_us-gaap_MortgageBackedSecuritiesOtherMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage-Backed Securities, Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesOtherMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MortgageBackedSecuritiesOtherMember"/>
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    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_5f924e41-6860-4ec1-a102-8d55b9ffb864_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in usd per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_bb8b46a4-2540-47c8-a5ac-dec54fae5311_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock (in usd per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
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    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_2e4f981a-601d-44db-b778-b2c495a4017f_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated useful life</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquired Finite-Lived Intangible Assets, Weighted Average Useful Life</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_8bbe3567-8bb8-4e8e-afca-14856d4b0f93_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-based Compensation Arrangements by Share-based Payment Award [Table]</link:label>
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    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_d79f6f31-5ce8-4997-9c32-9beef79237b0_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">CASH FLOWS FROM INVESTING ACTIVITIES:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities [Abstract]</link:label>
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    <link:label id="lab_fbc_MortgageLoansHeldForInvestmentMember_f5abbe5a-9764-41cb-a37f-78b9bfba65e1_terseLabel_en-US" xlink:label="lab_fbc_MortgageLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and Leases Held for Investment:</link:label>
    <link:label id="lab_fbc_MortgageLoansHeldForInvestmentMember_c7333f1e-d559-4c53-92b3-c084c0fc638c_verboseLabel_en-US" xlink:label="lab_fbc_MortgageLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Loans Held for Investment [Member]</link:label>
    <link:label id="lab_fbc_MortgageLoansHeldForInvestmentMember_label_en-US" xlink:label="lab_fbc_MortgageLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans Held for Investment [Member]</link:label>
    <link:label id="lab_fbc_MortgageLoansHeldForInvestmentMember_documentation_en-US" xlink:label="lab_fbc_MortgageLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans Held for Investment</link:label>
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    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
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    <link:label id="lab_us-gaap_JuniorSubordinatedDebentureOwedToUnconsolidatedSubsidiaryTrust_06e564db-06e9-411a-8939-08042719389d_terseLabel_en-US" xlink:label="lab_us-gaap_JuniorSubordinatedDebentureOwedToUnconsolidatedSubsidiaryTrust" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior subordinated debentures</link:label>
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    <link:label id="lab_us-gaap_PreferredStockLiquidationPreferenceValue_b589b03c-981f-4e6c-a351-ee5e9b37cd65_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreferenceValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Liquidation Preference, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockLiquidationPreferenceValue"/>
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    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFairValueOfNetAssetsAndLiabilitiesNet_5a609a42-ec71-4a7e-a55e-4a44cb195263_totalLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFairValueOfNetAssetsAndLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Fair value of net identifiable assets</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFairValueOfNetAssetsAndLiabilitiesNet_label_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentFairValueOfNetAssetsAndLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Fair Value of Net Assets and Liabilities, Net</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_f9954591-a93f-495b-9a6b-0616b2ebcf03_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Domain]</link:label>
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    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears_ae4e5bd8-7926-497e-a73c-26e4533f2113_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NoncumulativeConvertiblePreferredStockSeriesBMember" xlink:to="lab_fbc_NoncumulativeConvertiblePreferredStockSeriesBMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsumerLoanMember_bb18436b-6cd3-4a5d-8c4b-0c593ab9df87_terseLabel_en-US" xlink:label="lab_us-gaap_ConsumerLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Consumer</link:label>
    <link:label id="lab_us-gaap_ConsumerLoanMember_label_en-US" xlink:label="lab_us-gaap_ConsumerLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consumer Loan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsumerLoanMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConsumerLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsumerLoanMember" xlink:to="lab_us-gaap_ConsumerLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_afaae67d-af7d-4b7f-b3b3-0466933b4550_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_74cf6b90-f798-474a-9ccb-b19c31c4f883_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_90509674-213b-414b-91d6-bdf4118a4d3f_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquityAndEquitySharesOutstandingAbstract_7d676f19-cf9f-43c1-8b88-3392a8b5325a_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquitySharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares Outstanding</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquitySharesOutstandingAbstract_label_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquitySharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Shares Outstanding [Abstract]</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquitySharesOutstandingAbstract_documentation_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquitySharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquityAndEquitySharesOutstandingAbstract" xlink:href="fbc-20240630.xsd#fbc_TemporaryEquityAndEquitySharesOutstandingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_TemporaryEquityAndEquitySharesOutstandingAbstract" xlink:to="lab_fbc_TemporaryEquityAndEquitySharesOutstandingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_590cd783-69fd-4346-8402-67af0e0321b5_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rate lock commitments (net), measurement input</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeLiabilityMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:to="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationsAbstract_fbec43ab-82ae-4e33-a5b8-78a33cdeb52e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination:</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combinations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsAbstract" xlink:to="lab_us-gaap_BusinessCombinationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_IncreaseInDebtSecuritiesTrading_6ee9eb9a-8654-4480-99f0-025f70ee0f84_negatedTerseLabel_en-US" xlink:label="lab_fbc_IncreaseInDebtSecuritiesTrading" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of securities held for trading</link:label>
    <link:label id="lab_fbc_IncreaseInDebtSecuritiesTrading_label_en-US" xlink:label="lab_fbc_IncreaseInDebtSecuritiesTrading" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase in Debt Securities, Trading</link:label>
    <link:label id="lab_fbc_IncreaseInDebtSecuritiesTrading_documentation_en-US" xlink:label="lab_fbc_IncreaseInDebtSecuritiesTrading" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase in Debt Securities, Trading</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_IncreaseInDebtSecuritiesTrading" xlink:href="fbc-20240630.xsd#fbc_IncreaseInDebtSecuritiesTrading"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_IncreaseInDebtSecuritiesTrading" xlink:to="lab_fbc_IncreaseInDebtSecuritiesTrading" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_6c3a5e8a-778d-427b-a3b8-a29dde269db4_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated year one</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year One, Originated, Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextCallDateInNextRollingTwelveMonths_f3932428-0950-449b-bbed-275b79d65e4e_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextCallDateInNextRollingTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextCallDateInNextRollingTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextCallDateInNextRollingTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advances, Earlier of Contractual Maturity or Next Call Date, in Next Rolling 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextCallDateInNextRollingTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextCallDateInNextRollingTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextCallDateInNextRollingTwelveMonths" xlink:to="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextCallDateInNextRollingTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceInterestIncomeCashBasisMethod_69f2c366-8852-47ea-9ee4-56f40107a225_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceInterestIncomeCashBasisMethod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-accrual loans with an allowance recorded - Interest Income Recognized</link:label>
    <link:label id="lab_us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceInterestIncomeCashBasisMethod_label_en-US" xlink:label="lab_us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceInterestIncomeCashBasisMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impaired Financing Receivable, with Related Allowance, Interest Income, Cash Basis Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceInterestIncomeCashBasisMethod" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceInterestIncomeCashBasisMethod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceInterestIncomeCashBasisMethod" xlink:to="lab_us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceInterestIncomeCashBasisMethod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_5c73c2c1-ea0b-47fa-969d-68f2f7aa6258_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_322a4a6f-be1d-445e-ab3c-e034479371e9_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_051c5d6a-74fd-4a25-8513-13aaac5b052b_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Domain]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Balance [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BalanceSheetLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationDomain" xlink:to="lab_us-gaap_BalanceSheetLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleLineItems_bcbf7589-a339-4237-a1c0-e087227cfabd_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private-label Securitizations [Line Items]</link:label>
    <link:label id="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleLineItems_label_en-US" xlink:label="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securitization or Asset-Backed Financing Arrangement, Financial Asset for which Transfer is Accounted as Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleLineItems" xlink:to="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfAssetsAcquired_bf9f281b-7e74-4136-bd3f-624a10f39a8a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfAssetsAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of tangible assets acquired</link:label>
    <link:label id="lab_us-gaap_FairValueOfAssetsAcquired_label_en-US" xlink:label="lab_us-gaap_FairValueOfAssetsAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Assets Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfAssetsAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueOfAssetsAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOfAssetsAcquired" xlink:to="lab_us-gaap_FairValueOfAssetsAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesMember_4398ada7-30a3-4deb-9f86-b73b34b7fc1a_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities:</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesMember_80a73a25-d85c-4735-89f2-754598081694_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity securities:</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesMember_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquitySecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesMember" xlink:to="lab_us-gaap_EquitySecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_893ebb84-979e-4fb3-9497-1b3857c47df0_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
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    <link:label id="lab_us-gaap_DepositsSavingsDeposits_47b9056e-c02d-4006-a51c-7abc2958b2d6_terseLabel_en-US" xlink:label="lab_us-gaap_DepositsSavingsDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Savings accounts</link:label>
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    <link:label id="lab_fbc_PennFedCapitalTrustIIIMember_9869bb6b-f44a-411b-bd65-8c57ef40bb79_terseLabel_en-US" xlink:label="lab_fbc_PennFedCapitalTrustIIIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PennFed Capital Trust III</link:label>
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    <link:label id="lab_fbc_MultiFamilyAndCommercialRealEstateMember_22094c68-4ea4-41ba-afda-65f0f973bce3_terseLabel_en-US" xlink:label="lab_fbc_MultiFamilyAndCommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family and commercial real estate</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_0d71069d-6cd7-403b-bd8a-32628baf7ac7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Defined Benefit Plans Disclosures [Table]</link:label>
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    <link:label id="lab_srt_MaximumMember_a55420f2-939b-48de-ab92-a1779108c739_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesAbstract_32794552-4ffb-43e5-a8ad-c16f1d4c685f_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities available-for-sale</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AvailableForSaleSecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_8b02a1f1-c363-48b3-8cac-f7d284cd192f_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_LeaseFinancingLoansMember_f8aa0eb1-a927-4a50-b631-d2813e5922fe_terseLabel_en-US" xlink:label="lab_fbc_LeaseFinancingLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease financing</link:label>
    <link:label id="lab_fbc_LeaseFinancingLoansMember_label_en-US" xlink:label="lab_fbc_LeaseFinancingLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Financing Loans [Member]</link:label>
    <link:label id="lab_fbc_LeaseFinancingLoansMember_documentation_en-US" xlink:label="lab_fbc_LeaseFinancingLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Financing Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_LeaseFinancingLoansMember" xlink:href="fbc-20240630.xsd#fbc_LeaseFinancingLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_LeaseFinancingLoansMember" xlink:to="lab_fbc_LeaseFinancingLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_3bb3eeee-aa6b-404f-ac98-f34c31d5f629_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeAxis" xlink:to="lab_us-gaap_InvestmentTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion_02a19dda-7d2e-4381-85e5-1e91fb73c0d8_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued upon conversion (in shares)</link:label>
    <link:label id="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion_label_en-US" xlink:label="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Common Stock Issuable Upon Conversion</link:label>
    <link:label id="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion_documentation_en-US" xlink:label="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Common Stock Issuable Upon Conversion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:href="fbc-20240630.xsd#fbc_TemporaryEquitySharesCommonStockIssuableUponConversion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:to="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_f517db2c-cfbb-44c6-b683-3fb2da093c09_terseLabel_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued, price per share (in usd per share)</link:label>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_label_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesIssuedPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SharesIssuedPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesIssuedPricePerShare" xlink:to="lab_us-gaap_SharesIssuedPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleTable_047b6f6c-69d6-4ce5-829d-4b7797621087_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private-label Securitizations [Table]</link:label>
    <link:label id="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleTable_label_en-US" xlink:label="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Securitization or Asset-Backed Financing Arrangements, Financial Asset for which Transfer is Accounted as Sale [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleTable" xlink:to="lab_us-gaap_SecuritizationFinancialAssetForWhichTransferIsAccountedAsSaleTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCost_62d66a49-36ea-4af3-a9bf-4eb1efd67264_totalLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease cost</link:label>
    <link:label id="lab_us-gaap_LeaseCost_label_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCost" xlink:to="lab_us-gaap_LeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_3bc7e7e1-ee9a-4fd9-85f3-095c78984f4a_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_MortgageServicingRightsMember_688269d7-2db2-4f97-b8f5-5362c2b76611_terseLabel_en-US" xlink:label="lab_fbc_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights</link:label>
    <link:label id="lab_fbc_MortgageServicingRightsMember_label_en-US" xlink:label="lab_fbc_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights [Member]</link:label>
    <link:label id="lab_fbc_MortgageServicingRightsMember_documentation_en-US" xlink:label="lab_fbc_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative assets or liabilities which hedge the risk of overall changes in fair value of MSRs through the use of various derivatives including purchases of forward contracts on securities of Fannie Mae and Freddie Mac, the purchase/sale of U.S. Treasury futures contracts and the purchase/sale of euro dollar future contracts. These are accounted for as non-designated hedges.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_MortgageServicingRightsMember" xlink:href="fbc-20240630.xsd#fbc_MortgageServicingRightsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_MortgageServicingRightsMember" xlink:to="lab_fbc_MortgageServicingRightsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorLeaseDescriptionLineItems_80d057d8-c3a2-46d3-ae6e-42d353a57c25_terseLabel_en-US" xlink:label="lab_us-gaap_LessorLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessor, Lease, Description [Line Items]</link:label>
    <link:label id="lab_us-gaap_LessorLeaseDescriptionLineItems_label_en-US" xlink:label="lab_us-gaap_LessorLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Lease, Description [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorLeaseDescriptionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LessorLeaseDescriptionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorLeaseDescriptionLineItems" xlink:to="lab_us-gaap_LessorLeaseDescriptionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_0edd85cf-5f8d-404c-bb00-160f78a9974b_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">(Loss) income before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_5ad68b30-c67c-48c2-baf1-88e6d364fe68_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncumulative convertible preferred stock (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquitySharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:to="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract_6ae61083-d981-46d1-93d6-7de60f9f4cc5_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current-period gross write-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Writeoff, by Origination Year [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract"/>
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    <link:label id="lab_fbc_AOCIDebtSecuritiesAvailableForSaleAdjustmentTax_841e87c5-2459-4d2a-929c-d19c8e96e5b9_terseLabel_en-US" xlink:label="lab_fbc_AOCIDebtSecuritiesAvailableForSaleAdjustmentTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized loss on securities available for sale, tax</link:label>
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    <link:label id="lab_us-gaap_CorporateNoteSecuritiesMember_d63e53e2-382b-4e88-b299-8d47ea3293d7_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNoteSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital trust notes</link:label>
    <link:label id="lab_us-gaap_CorporateNoteSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_CorporateNoteSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Note Securities [Member]</link:label>
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    <link:label id="lab_fbc_NoncumulativePreferredStockSeriesAMember_39f718cd-b700-4866-886e-c532eb10cfe3_terseLabel_en-US" xlink:label="lab_fbc_NoncumulativePreferredStockSeriesAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncumulative Series A Preferred Stock</link:label>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearTwo_33d4307b-4124-404a-93c2-0a4734d2e395_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
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    <link:label id="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember_8d6d12d7-c95d-4fa0-85b1-a2acc1162c94_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Constant prepayment rate</link:label>
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    <link:label id="lab_fbc_SpecialtyFinanceLoansAndLeasesMember_1ab38e37-3f4c-4b20-b2bb-a4b61023bed4_terseLabel_en-US" xlink:label="lab_fbc_SpecialtyFinanceLoansAndLeasesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Specialty finance loans and leases</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PvpTable"/>
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    <link:label id="lab_stpr_CT_1a3b2b3e-87be-44e1-96bd-7364ddfc5f55_terseLabel_en-US" xlink:label="lab_stpr_CT" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Connecticut</link:label>
    <link:label id="lab_stpr_CT_label_en-US" xlink:label="lab_stpr_CT" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CONNECTICUT</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_40043588-3da2-4f74-bda8-0dcc4c40019e_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Outstanding, beginning balance (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_be45a8e7-0e2e-4032-a76e-026d12e84255_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Outstanding, ending balance (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_b557b794-1531-414a-86bb-2b619a8bc0b5_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease right-of-use assets</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_f1d9b66b-9ed1-489c-883e-6964fae13574_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_dc4ae31e-e767-46fe-8f2b-21154d7af473_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Outstanding, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_9aa0fe75-c92c-423d-b882-c07ee6d9008e_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Outstanding, ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
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    <link:label id="lab_fbc_SensitivityAnalysisofFairValueTransferorsInterestsinTransferredFinancialAssetsImpactofOtherthan10or20PercentAdverseChangeinOptionAdjustedSpreadPercent_2a8de32a-bc0d-47ed-81e6-f3116acd7bf6_terseLabel_en-US" xlink:label="lab_fbc_SensitivityAnalysisofFairValueTransferorsInterestsinTransferredFinancialAssetsImpactofOtherthan10or20PercentAdverseChangeinOptionAdjustedSpreadPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Option adjusted spread (percent)</link:label>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMember_095a063e-2c9d-425b-af51-068e9cd73761_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FHLB advances</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMember_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank Advances [Member]</link:label>
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    <link:label id="lab_us-gaap_TemporaryEquityByClassOfStockTable_934b437b-f6e2-4c33-bf80-70763c715868_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityByClassOfStockTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityByClassOfStockTable"/>
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    <link:label id="lab_stpr_CA_626f20eb-fcce-44a1-9f86-d660616182d7_terseLabel_en-US" xlink:label="lab_stpr_CA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">California</link:label>
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    <link:label id="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1_dc133d6d-fbe4-4813-975f-e284c96041d8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gain on loan sales</link:label>
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    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLoansHeldForInvestment_807c1bb8-32fe-4582-9835-6ee8f5004e55_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total loans held for investment</link:label>
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    <link:label id="lab_us-gaap_OtherCommitmentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1_30b9cb1b-c08b-4228-8b7a-307aedf41036_terseLabel_en-US" xlink:label="lab_us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer of loans from held for investment to held for sale</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1"/>
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    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_0c9c53a5-bce4-4065-83a5-a61a79a632d2_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Axis]</link:label>
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    <link:label id="lab_us-gaap_TreasuryStockCommonValue_fb688608-c345-48ce-a89b-dc6ca2189f01_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock, at cost (7,560,100 and 7,363,140 shares, respectively)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TreasuryStockCommonValue"/>
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    <link:label id="lab_fbc_DecreaseInDebtSecuritiesTrading_58409f0f-ec60-44ad-ae46-dae9d5fbb0ce_terseLabel_en-US" xlink:label="lab_fbc_DecreaseInDebtSecuritiesTrading" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of securities held for trading</link:label>
    <link:label id="lab_fbc_DecreaseInDebtSecuritiesTrading_label_en-US" xlink:label="lab_fbc_DecreaseInDebtSecuritiesTrading" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Decrease in Debt Securities, Trading</link:label>
    <link:label id="lab_fbc_DecreaseInDebtSecuritiesTrading_documentation_en-US" xlink:label="lab_fbc_DecreaseInDebtSecuritiesTrading" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Decrease in Debt Securities, Trading</link:label>
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    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_f282a5ec-d68d-49f7-84c9-23333faa87f5_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and leases</link:label>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_label_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Fee Income, Loans and Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestAndFeeIncomeLoansAndLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:to="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember_b245a9ba-2601-40f4-b975-7a7beb0d824e_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based payment arrangement, tranche three</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Tranche Three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationAwardTrancheThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:to="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
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    <link:label id="lab_us-gaap_PerformingFinancingReceivableMember_8a2670a0-3528-48de-baa4-a98f55cb05e5_verboseLabel_en-US" xlink:label="lab_us-gaap_PerformingFinancingReceivableMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total other performing loans</link:label>
    <link:label id="lab_us-gaap_PerformingFinancingReceivableMember_label_en-US" xlink:label="lab_us-gaap_PerformingFinancingReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performing Financial Instruments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformingFinancingReceivableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PerformingFinancingReceivableMember"/>
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    <link:label id="lab_us-gaap_SharesOutstanding_6fb8c433-6765-45fd-92c4-20f70b97e6e0_periodStartLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesOutstanding_397ecff3-95e3-499f-8f97-d783e03a9579_periodEndLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesOutstanding_label_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesOutstanding" xlink:to="lab_us-gaap_SharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_5cfa097b-0ba8-40fb-ac13-59615d6b854b_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
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    <link:label id="lab_fbc_AcquisitionDevelopmentAndConstructionLoanMember_4d89183e-a077-45cb-882a-c1e87613a78a_terseLabel_en-US" xlink:label="lab_fbc_AcquisitionDevelopmentAndConstructionLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition, development, and construction</link:label>
    <link:label id="lab_fbc_AcquisitionDevelopmentAndConstructionLoanMember_label_en-US" xlink:label="lab_fbc_AcquisitionDevelopmentAndConstructionLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquisition, Development, and Construction Loan [Member]</link:label>
    <link:label id="lab_fbc_AcquisitionDevelopmentAndConstructionLoanMember_documentation_en-US" xlink:label="lab_fbc_AcquisitionDevelopmentAndConstructionLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Acquisition, Development, and Construction Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_AcquisitionDevelopmentAndConstructionLoanMember" xlink:href="fbc-20240630.xsd#fbc_AcquisitionDevelopmentAndConstructionLoanMember"/>
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    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AggtErrCompAmt"/>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract_99766369-73bb-48c3-930c-221c207963af_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advances, Par Value, Earlier of Contractual Maturity or Next Put or Convert Date, Rolling Year [Abstract]</link:label>
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    <link:label id="lab_dei_LocalPhoneNumber_ea6466bd-4dbc-43f9-a781-23093b93ff1b_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_LocalPhoneNumber"/>
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    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_a4e29c71-5760-458d-a479-cd999214e9c5_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Carrying Amount</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Gross (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IntangibleAssetsGrossExcludingGoodwill"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract_ae58fc5c-5dcf-4d9e-a886-952182fb4662_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of liabilities assumed:</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_a4df494e-64ed-4306-81f1-309f8825c436_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for (recovery of) credit losses on loans and leases</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal"/>
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    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCertificatesOfDeposit_14ca8e5e-4975-4cd5-afe0-5f8496e9f256_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCertificatesOfDeposit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Certificates of deposit</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoanWriteoff_b4714ba1-6d51-4308-bb3b-78ed4795f058_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingConvertedToTermLoanWriteoff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Revolving Loans Converted to Term Loans</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_67b9f2ae-8137-48ec-8cb1-c758e58157b2_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated year five</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_3b99e640-166a-4482-a4a8-d574ee05fb80_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
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    <link:label id="lab_us-gaap_OccupancyNet_17d7f4fe-f8fe-4258-bb18-b5b6f855d4d9_terseLabel_en-US" xlink:label="lab_us-gaap_OccupancyNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Occupancy and equipment</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_bbe03905-ba13-4a7f-90ae-59d41d04bcc3_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued (in shares)</link:label>
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    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCost_930900f0-f99a-4ae4-b99c-dd2888a8349d_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_0906acef-a6d5-4201-ac00-b61144e8e808_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_8949c613-2c59-42d4-81c3-e2816ad80068_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total debt securities available for sale</link:label>
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    <link:label id="lab_us-gaap_LessorLeaseDescriptionTable_98d9ad39-09f7-49f9-9b6d-f04903968f7e_terseLabel_en-US" xlink:label="lab_us-gaap_LessorLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessor, Lease, Description [Table]</link:label>
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    <link:label id="lab_fbc_AOCICashFlowHedgeCumulativeGainLossTax_documentation_en-US" xlink:label="lab_fbc_AOCICashFlowHedgeCumulativeGainLossTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AOCI, Cash Flow Hedge, Cumulative Gain (Loss), Tax</link:label>
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    <link:label id="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember_47e53e70-4b2a-4d7c-ae3f-99a64967af65_terseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GSE debentures</link:label>
    <link:label id="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government-sponsored Enterprises Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember"/>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_5e5ab438-ad13-4021-8d3d-c49ef777e1e0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_CommonStockMember_b5c0f69b-979f-49d2-8140-2e4968567189_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock (Par Value: $0.01)</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockMember"/>
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    <link:label id="lab_fbc_BusinessCombinationBargainPurchaseGainRecognizedNetOfAdjustmentsAmount_documentation_en-US" xlink:label="lab_fbc_BusinessCombinationBargainPurchaseGainRecognizedNetOfAdjustmentsAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Bargain Purchase, Gain Recognized, Net Of Adjustments, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BusinessCombinationBargainPurchaseGainRecognizedNetOfAdjustmentsAmount" xlink:href="fbc-20240630.xsd#fbc_BusinessCombinationBargainPurchaseGainRecognizedNetOfAdjustmentsAmount"/>
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    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_60c95009-aeb9-4ed9-8397-efe0ff79e00e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral Pledged (Received)</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Cash Not Offset</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:to="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_b067d4b1-d020-4204-b8f2-e75c3beac50b_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reverse stock split</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Note, Stock Split, Conversion Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquityNoteStockSplitConversionRatio1"/>
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    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther_2e27f2c4-4c25-430a-9e55-9a2a81c50980_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther"/>
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    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_10af93c0-d8b9-42ef-9818-f07068f54e7d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Business Acquisitions, by Acquisition [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Business Acquisitions, by Acquisition [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
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    <link:label id="lab_us-gaap_GainLossOnSaleOfNotesReceivable_ea50e3bb-30e3-4ac9-99e8-e064d6c9e2bf_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net gain on sales of loans</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfNotesReceivable_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Financing Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainLossOnSaleOfNotesReceivable"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfTreasuryStock_b0b4995f-c9c7-42f9-b070-9e02980f8b96_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfTreasuryStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Re-issuance of treasury stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfTreasuryStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfTreasuryStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Treasury Stock</link:label>
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    <link:label id="lab_dei_EntityCentralIndexKey_ea2a0538-59bf-409a-a2e8-a65ce8d20bdc_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
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    <link:label id="lab_srt_StatementScenarioAxis_label_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_StatementScenarioAxis"/>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesFloatingRateAbstract_1e458eee-8f7e-4938-b004-7c438d008704_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesFloatingRateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contractual Maturity</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesFloatingRateAbstract_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesFloatingRateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advances, Floating Rate [Abstract]</link:label>
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    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
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    <link:label id="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetBeforeFairValueAdjustments_c5d62a9d-47bd-42fa-9930-7fb484da2d43_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetBeforeFairValueAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net assets acquired before fair value adjustments</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_c555f362-bdc8-41dd-a220-fa2e9d8ee538_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember_69ffa347-2c0e-43d0-9790-20cb8fc939a4_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Actuarial losses</link:label>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Defined Benefit Plans Adjustment, Net Gain (Loss) Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:to="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OtherCollateralMember_36145e35-06ee-4f9e-aa62-127f0e0f6569_terseLabel_en-US" xlink:label="lab_fbc_OtherCollateralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_fbc_OtherCollateralMember_label_en-US" xlink:label="lab_fbc_OtherCollateralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Collateral [Member]</link:label>
    <link:label id="lab_fbc_OtherCollateralMember_documentation_en-US" xlink:label="lab_fbc_OtherCollateralMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Collateral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OtherCollateralMember" xlink:href="fbc-20240630.xsd#fbc_OtherCollateralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OtherCollateralMember" xlink:to="lab_fbc_OtherCollateralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_30ec0b2e-84c8-484d-af2b-deb0a5665e94_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation expense related to restricted stock awards</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockMember_7a6c329c-2b67-4d27-8cee-35febd305226_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockMember" xlink:to="lab_us-gaap_RestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_3e94aa52-d127-4f7d-a8d4-b427bcefac52_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_d0402bf2-d826-456f-ac13-567cc8ab3b5a_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and leases held for investment, net</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:to="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_CommercialLettersOfCreditMember_a3c6c6a7-3c1f-4987-9145-7dff85117478_terseLabel_en-US" xlink:label="lab_fbc_CommercialLettersOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial letters of credit</link:label>
    <link:label id="lab_fbc_CommercialLettersOfCreditMember_label_en-US" xlink:label="lab_fbc_CommercialLettersOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial, Letters Of Credit [Member]</link:label>
    <link:label id="lab_fbc_CommercialLettersOfCreditMember_documentation_en-US" xlink:label="lab_fbc_CommercialLettersOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial, Letters Of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_CommercialLettersOfCreditMember" xlink:href="fbc-20240630.xsd#fbc_CommercialLettersOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_CommercialLettersOfCreditMember" xlink:to="lab_fbc_CommercialLettersOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_2c4f35ad-3bbc-487a-904b-f17686518a1e_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRestricted_1f73bed8-1349-4d35-9d4d-de1cc35c3b79_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRestricted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged investment securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRestricted_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRestricted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Restricted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRestricted" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtSecuritiesAvailableForSaleRestricted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRestricted" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRestricted" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_ServicingAssetatFairValueIncomeAmount_9506c4e5-6fe1-4c93-bc23-90f55ba8488f_terseLabel_en-US" xlink:label="lab_fbc_ServicingAssetatFairValueIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total return (loss) included in net return on mortgage servicing rights</link:label>
    <link:label id="lab_fbc_ServicingAssetatFairValueIncomeAmount_label_en-US" xlink:label="lab_fbc_ServicingAssetatFairValueIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Income, Amount</link:label>
    <link:label id="lab_fbc_ServicingAssetatFairValueIncomeAmount_documentation_en-US" xlink:label="lab_fbc_ServicingAssetatFairValueIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The total amount of income earned on loans serviced and subserviced for others during the period for which results of operations are presented.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ServicingAssetatFairValueIncomeAmount" xlink:href="fbc-20240630.xsd#fbc_ServicingAssetatFairValueIncomeAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_ServicingAssetatFairValueIncomeAmount" xlink:to="lab_fbc_ServicingAssetatFairValueIncomeAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember_2db4e99a-3096-4400-943d-775e1df96a1b_terseLabel_en-US" xlink:label="lab_fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total wholesale borrowings</link:label>
    <link:label id="lab_fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember_label_en-US" xlink:label="lab_fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank Advances And Federal Reserve Bank Funding [Member]</link:label>
    <link:label id="lab_fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember_documentation_en-US" xlink:label="lab_fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank Advances And Federal Reserve Bank Funding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember" xlink:href="fbc-20240630.xsd#fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember" xlink:to="lab_fbc_FederalHomeLoanBankAdvancesAndFederalReserveBankFundingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_68407508-38d9-4bbe-b81f-a39b46c70c3d_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_e432a13c-5c9b-4e47-9212-00b6826ffae5_terseLabel_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total loan commitments</link:label>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_label_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unfunded Loan Commitment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnfundedLoanCommitmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:to="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock_fd294852-f489-493c-8b4f-0df646db7c0c_terseLabel_en-US" xlink:label="lab_fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income and Fees</link:label>
    <link:label id="lab_fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock_label_en-US" xlink:label="lab_fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Servicing Assets at Fair Value, Servicing Fees [Table Text Block]</link:label>
    <link:label id="lab_fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock_documentation_en-US" xlink:label="lab_fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of contractual servicing fees, including late fees and ancillary income, for each type of loan serviced.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock" xlink:href="fbc-20240630.xsd#fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock" xlink:to="lab_fbc_ScheduleOfServicingAssetsAtFairValueServicingFeesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherNetAssetsAndLiabilities_abb5bb36-8547-4b15-aae5-9b76c605ea34_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherNetAssetsAndLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other net assets and liabilities</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherNetAssetsAndLiabilities_label_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherNetAssetsAndLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Other Net Assets And Liabilities</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherNetAssetsAndLiabilities_documentation_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherNetAssetsAndLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Other Net Assets And Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherNetAssetsAndLiabilities" xlink:href="fbc-20240630.xsd#fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherNetAssetsAndLiabilities"/>
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    <link:label id="lab_us-gaap_BankOwnedLifeInsurance_d6a5af49-dd28-4ecf-b7a9-33efc27ea323_verboseLabel_en-US" xlink:label="lab_us-gaap_BankOwnedLifeInsurance" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Bank-owned life insurance</link:label>
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    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairedFinancingReceivablesTableTextBlock_1c3d5ade-e93c-4723-aeeb-cde9ca3012e4_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairedFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Additional Information about Nonaccrual Loans</link:label>
    <link:label id="lab_us-gaap_ImpairedFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ImpairedFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impaired Financing Receivables [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairedFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ImpairedFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairedFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_ImpairedFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_129980cf-4ed3-4007-bd53-341f08749372_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_f4f2d69c-909b-4857-a677-9720b389ec13_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OtherLoanCommitmentsMember_e5a2ce1a-3008-4a85-ae18-bfe48fe6d700_terseLabel_en-US" xlink:label="lab_fbc_OtherLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other loan commitments</link:label>
    <link:label id="lab_fbc_OtherLoanCommitmentsMember_label_en-US" xlink:label="lab_fbc_OtherLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Loan Commitments [Member]</link:label>
    <link:label id="lab_fbc_OtherLoanCommitmentsMember_documentation_en-US" xlink:label="lab_fbc_OtherLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Loan Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OtherLoanCommitmentsMember" xlink:href="fbc-20240630.xsd#fbc_OtherLoanCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OtherLoanCommitmentsMember" xlink:to="lab_fbc_OtherLoanCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_b75ae551-dc84-41d5-b43f-ac353e906962_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_93e54bd3-339b-4888-85e5-492cef2a27e5_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total present value of lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OneToFourFamilyFirstMortgageLoanMember_75566ad2-8760-4670-a0ad-d017ce217f2e_terseLabel_en-US" xlink:label="lab_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">One-to-four family first mortgage</link:label>
    <link:label id="lab_fbc_OneToFourFamilyFirstMortgageLoanMember_label_en-US" xlink:label="lab_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">One-to-Four Family First Mortgage Loan [Member]</link:label>
    <link:label id="lab_fbc_OneToFourFamilyFirstMortgageLoanMember_documentation_en-US" xlink:label="lab_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">One-to-Four Family First Mortgage Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:href="fbc-20240630.xsd#fbc_OneToFourFamilyFirstMortgageLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:to="lab_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_51810ac5-dbf0-48a4-a28b-8411fd7ab195_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Investment Securities</link:label>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract_87953a77-30e7-468a-a210-70569c4ffb9e_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount Outstanding (in millions)</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract_label_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Amount Outstanding, Value [Abstract]</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract_documentation_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Amount Outstanding, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract" xlink:href="fbc-20240630.xsd#fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract" xlink:to="lab_fbc_TemporaryEquityAndEquityAmountOutstandingValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConversionOfStockNameDomain_30f311e6-602a-4059-80ef-73d2989f1ba2_terseLabel_en-US" xlink:label="lab_us-gaap_ConversionOfStockNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_ConversionOfStockNameDomain_label_en-US" xlink:label="lab_us-gaap_ConversionOfStockNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConversionOfStockNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConversionOfStockNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConversionOfStockNameDomain" xlink:to="lab_us-gaap_ConversionOfStockNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_5ee3e8fa-d8a9-488c-8477-2cdfbbae0540_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_dffb045c-b962-4a32-817d-d6d5c5f21084_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubordinatedDebtMember_9af7d0bb-67a9-44ce-a683-85828184cb81_terseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated notes</link:label>
    <link:label id="lab_us-gaap_SubordinatedDebtMember_label_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubordinatedDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubordinatedDebtMember" xlink:to="lab_us-gaap_SubordinatedDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FederalReserveBankDiscountMember_6d2a1b18-82ad-4d6a-80ce-9a9e7c575028_terseLabel_en-US" xlink:label="lab_fbc_FederalReserveBankDiscountMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal Reserve Bank Discount Window</link:label>
    <link:label id="lab_fbc_FederalReserveBankDiscountMember_label_en-US" xlink:label="lab_fbc_FederalReserveBankDiscountMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Reserve Bank Discount [Member]</link:label>
    <link:label id="lab_fbc_FederalReserveBankDiscountMember_documentation_en-US" xlink:label="lab_fbc_FederalReserveBankDiscountMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Federal Reserve Bank Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FederalReserveBankDiscountMember" xlink:href="fbc-20240630.xsd#fbc_FederalReserveBankDiscountMember"/>
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    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_1e8abf62-e3c5-4b7c-a331-33b291e10cd7_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock Mezzanine (Par Value: $0.01)</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
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    <link:label id="lab_fbc_EquitySecuritiesUnrealizedLoss_13b56896-140e-478b-a26b-898a5ac7b93c_terseLabel_en-US" xlink:label="lab_fbc_EquitySecuritiesUnrealizedLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Unrealized Loss</link:label>
    <link:label id="lab_fbc_EquitySecuritiesUnrealizedLoss_label_en-US" xlink:label="lab_fbc_EquitySecuritiesUnrealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, Unrealized Loss</link:label>
    <link:label id="lab_fbc_EquitySecuritiesUnrealizedLoss_documentation_en-US" xlink:label="lab_fbc_EquitySecuritiesUnrealizedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities, Unrealized Loss</link:label>
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    <link:label id="lab_us-gaap_FederalDepositInsuranceCorporationPremiumExpense_8c5607a2-fb60-441a-92f1-2446261527d1_terseLabel_en-US" xlink:label="lab_us-gaap_FederalDepositInsuranceCorporationPremiumExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FDIC insurance</link:label>
    <link:label id="lab_us-gaap_FederalDepositInsuranceCorporationPremiumExpense_label_en-US" xlink:label="lab_us-gaap_FederalDepositInsuranceCorporationPremiumExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Deposit Insurance Corporation Premium Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalDepositInsuranceCorporationPremiumExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalDepositInsuranceCorporationPremiumExpense"/>
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    <link:label id="lab_us-gaap_ScheduleOfInvestmentsTable_56c79d77-7d2a-4565-8500-418d68a01c98_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_RateLockCommitmentsAndUSTreasuryFuturesMember_465589d3-533b-4d29-af96-68ad1b409780_terseLabel_en-US" xlink:label="lab_fbc_RateLockCommitmentsAndUSTreasuryFuturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rate lock commitments and US Treasury futures</link:label>
    <link:label id="lab_fbc_RateLockCommitmentsAndUSTreasuryFuturesMember_label_en-US" xlink:label="lab_fbc_RateLockCommitmentsAndUSTreasuryFuturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rate Lock Commitments And U.S. Treasury Futures [Member]</link:label>
    <link:label id="lab_fbc_RateLockCommitmentsAndUSTreasuryFuturesMember_documentation_en-US" xlink:label="lab_fbc_RateLockCommitmentsAndUSTreasuryFuturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rate Lock Commitments And U.S. Treasury Futures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_RateLockCommitmentsAndUSTreasuryFuturesMember" xlink:href="fbc-20240630.xsd#fbc_RateLockCommitmentsAndUSTreasuryFuturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_RateLockCommitmentsAndUSTreasuryFuturesMember" xlink:to="lab_fbc_RateLockCommitmentsAndUSTreasuryFuturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_eb39dfb0-eab1-40e8-886e-0eeb37c6c283_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other changes in loans, net</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Other Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
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    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
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    <link:label id="lab_us-gaap_ProvisionForLoanLossesExpensed_fa98b6e4-b57d-4539-85f7-8333427e8e5e_terseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLossesExpensed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for credit losses</link:label>
    <link:label id="lab_us-gaap_ProvisionForLoanLossesExpensed_label_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLossesExpensed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Loss, Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForLoanLossesExpensed" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProvisionForLoanLossesExpensed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForLoanLossesExpensed" xlink:to="lab_us-gaap_ProvisionForLoanLossesExpensed" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SensitivityAnalysisOfFairValuesTransferorsInterestsInTransferredFinancialAssetsImpactOfOtherThan10Or20PercentAdverseChangeInOtherAssumptionPerLoan_c4651bcc-9c9e-47f5-ac7b-7923eb7a4666_terseLabel_en-US" xlink:label="lab_fbc_SensitivityAnalysisOfFairValuesTransferorsInterestsInTransferredFinancialAssetsImpactOfOtherThan10Or20PercentAdverseChangeInOtherAssumptionPerLoan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average cost to service per loan</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_fbc_SensitivityAnalysisOfFairValuesTransferorsInterestsInTransferredFinancialAssetsImpactOfOtherThan10Or20PercentAdverseChangeInOtherAssumptionPerLoan" xlink:href="fbc-20240630.xsd#fbc_SensitivityAnalysisOfFairValuesTransferorsInterestsInTransferredFinancialAssetsImpactOfOtherThan10Or20PercentAdverseChangeInOtherAssumptionPerLoan"/>
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    <link:label id="lab_fbc_OtherLoansHeldForInvestmentMember_46dc2cd1-6bed-431a-be28-44dec2df17c4_terseLabel_en-US" xlink:label="lab_fbc_OtherLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other loans held for investment</link:label>
    <link:label id="lab_fbc_OtherLoansHeldForInvestmentMember_6710eca5-c72f-43cf-81b9-163ab20fd38c_verboseLabel_en-US" xlink:label="lab_fbc_OtherLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_fbc_OtherLoansHeldForInvestmentMember_a64984fa-30cf-40db-ac21-21fbbd061178_netLabel_en-US" xlink:label="lab_fbc_OtherLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Other (includes commercial and industrial)</link:label>
    <link:label id="lab_fbc_OtherLoansHeldForInvestmentMember_label_en-US" xlink:label="lab_fbc_OtherLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Loans Held for Investment [Member]</link:label>
    <link:label id="lab_fbc_OtherLoansHeldForInvestmentMember_documentation_en-US" xlink:label="lab_fbc_OtherLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Loans Held for Investment</link:label>
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    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
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    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_74684a9c-80bf-4586-bff4-ac35ae53852e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, amount of hedged item</link:label>
    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_label_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Amount of Hedged Item</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAmountOfHedgedItem" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeAmountOfHedgedItem"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAmountOfHedgedItem" xlink:to="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_CashFlowLesseeAbstract_cbebce4a-72e1-4551-a359-d4b08bd5db6f_terseLabel_en-US" xlink:label="lab_fbc_CashFlowLesseeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for amounts included in the measurement of lease liabilities:</link:label>
    <link:label id="lab_fbc_CashFlowLesseeAbstract_label_en-US" xlink:label="lab_fbc_CashFlowLesseeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow, Lessee [Abstract]</link:label>
    <link:label id="lab_fbc_CashFlowLesseeAbstract_documentation_en-US" xlink:label="lab_fbc_CashFlowLesseeAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash Flow, Lessee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_CashFlowLesseeAbstract" xlink:href="fbc-20240630.xsd#fbc_CashFlowLesseeAbstract"/>
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    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_ef982e8d-1e64-4d3b-b8ff-415f6cc8f9e3_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Bargain purchase gain</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_60062f01-fad2-40eb-a67b-02f5d361c014_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bargain purchase gain on Signature Transaction, as initially reported</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Bargain Purchase, Gain Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_b12df731-04fc-4651-8dfa-ff7f3afaf47f_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_7d2f8cd5-5837-4654-a5b7-92ac0d702f83_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Options</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward"/>
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    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
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    <link:label id="lab_us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceRecordedInvestment_9e98bf77-36b8-45dc-a7b5-680af5311261_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceRecordedInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-accrual loans with an allowance recorded - Recorded Investment</link:label>
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    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities_a3dd4477-6ed7-48ce-b089-8b5fc74b0484_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities_label_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Other Liabilities</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities_documentation_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities" xlink:href="fbc-20240630.xsd#fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities" xlink:to="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_e0738547-fbbd-43e1-adca-a9e247c8b474_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash acquired in business acquisition</link:label>
    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_label_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Acquired from Acquisition</link:label>
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    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_5a7c9fe7-587c-433e-9601-92bd0037b796_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis"/>
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    <link:label id="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable_702f40c8-f35f-444d-8f10-1fd2035fd12c_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation, Less than Wholly Owned Subsidiary, Parent Ownership Interest, Effects of Changes, Net [Table]</link:label>
    <link:label id="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable_label_en-US" xlink:label="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Less-than-Wholly-Owned Subsidiary, Parent Ownership Interest, Effect of Change [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable"/>
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    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_f42796ce-2755-40fc-b428-c3ce69aadf3d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetsAbstract" xlink:to="lab_us-gaap_DerivativeAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRateMaturingInRollingYearFour_570c296d-281f-4b7a-9a3b-5dfe3362a544_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRateMaturingInRollingYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRateMaturingInRollingYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRateMaturingInRollingYearFour"/>
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    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_4d35d3df-3008-40da-bce6-bbe589ed338a_terseLabel_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives designated hedging instruments:</link:label>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_label_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Designated as Hedging Instrument [Member]</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_c55b4e26-286e-48b6-a864-82fbd761c35e_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income available to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_be8fde8b-9317-42d8-8b14-fd48a410cbd0_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income available to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
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    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
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    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
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    <link:label id="lab_us-gaap_SecuritiesBorrowedAbstract_362cfaa8-f338-429d-a8ee-78b0eb69544e_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesBorrowedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowed funds:</link:label>
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    <link:label id="lab_us-gaap_Assets_bfa2a3e7-1c37-475e-befa-24a298820d59_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Assets"/>
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    <link:label id="lab_fbc_GainLossOnSaleOfFinancingReceivableMember_6ccbc86d-4666-4376-a737-182a462ba266_terseLabel_en-US" xlink:label="lab_fbc_GainLossOnSaleOfFinancingReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gain on loan sales</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfServicingAssetsAtFairValueTextBlock_af4152d0-03ee-449d-8bfb-f18b211d3dd1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfServicingAssetsAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in the Fair Value of Residential First Mortgage MSRs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Debt Securities, Available-for-Sale, Adjustment, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax"/>
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    <link:label id="lab_fbc_SharesIssuedPricePerShareSplitAdjustedBasis_f298c4e8-145d-42a5-8456-b7b78bc1cbcc_terseLabel_en-US" xlink:label="lab_fbc_SharesIssuedPricePerShareSplitAdjustedBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued price per share split adjusted basis (in usd per share)</link:label>
    <link:label id="lab_fbc_SharesIssuedPricePerShareSplitAdjustedBasis_label_en-US" xlink:label="lab_fbc_SharesIssuedPricePerShareSplitAdjustedBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued Price Per Share Split Adjusted Basis</link:label>
    <link:label id="lab_fbc_SharesIssuedPricePerShareSplitAdjustedBasis_documentation_en-US" xlink:label="lab_fbc_SharesIssuedPricePerShareSplitAdjustedBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Shares Issued Price Per Share Split Adjusted Basis</link:label>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_7c7674a8-f7e2-4ef2-a370-302b070a4cea_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesMember_93883496-501f-4307-bb83-fa3fa56b23a8_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage-Related Debt Securities:</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesMember_7231d95c-3f07-4f4e-826b-c7495b3f8533_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage-related Debt Securities Available for Sale:</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Mortgage-Backed Securities [Member]</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_7040b3b9-2b74-4427-a9ca-e8982d0dcf41_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableImpairedLineItems_69b927be-2a3b-4c78-9b12-9b4009faced7_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableImpairedLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Impaired [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableImpairedLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableImpairedLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Impaired [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableImpairedLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableImpairedLineItems"/>
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    <link:label id="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCoreDepositAndOtherIntangibleAssets_8d17b297-0352-47b8-a0dd-c82843b014a9_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCoreDepositAndOtherIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CDI and other intangible assets</link:label>
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    <link:label id="lab_us-gaap_SensitivityAnalysisOfFairValueOfInterestsContinuedToBeHeldByTransferorServicingAssetsOrLiabilitiesImpactOfOtherThan10Or20PercentAdverseChangeInPrepaymentSpeedPercent_0db9642e-b9f5-4f43-98e9-a274142393b4_terseLabel_en-US" xlink:label="lab_us-gaap_SensitivityAnalysisOfFairValueOfInterestsContinuedToBeHeldByTransferorServicingAssetsOrLiabilitiesImpactOfOtherThan10Or20PercentAdverseChangeInPrepaymentSpeedPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Constant prepayment rate (as a percent)</link:label>
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    <link:label id="lab_us-gaap_MarketableSecuritiesAbstract_2fbb7376-1cdf-4b77-bfb6-76bb2bd35d34_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Securities</link:label>
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    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
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    <link:label id="lab_us-gaap_NondesignatedMember_3ed0f52a-d90d-4111-af1b-c8ccd96f88ec_terseLabel_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives not designated as hedging instruments:</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfMortgageServicingRightsMSR_d6f14920-6a7c-4f05-8218-c2fe8d57237b_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds from sales of mortgage servicing rights</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentAxis_43985a57-d6e3-4ece-bcfc-89623d693c59_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentAxis"/>
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    <link:label id="lab_us-gaap_TemporaryEquityTableTextBlock_488991da-8a87-4179-adab-a1089765c3f3_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Temporary Equity</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityTableTextBlock"/>
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    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_c9135a31-b0ee-45a9-a12c-82707c9f9d63_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral Pledged (Received)</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLoss_03908958-4ee1-42fd-9d37-19bd4b0fd6a1_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_94de19c8-6f50-4902-9440-3bee7368fcd4_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_b5c08954-cd18-427f-ad03-d8c2530fbb9f_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
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    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
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    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_84919280-88b6-403d-b55b-405dba9da404_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Carrying Amount and Estimated Fair Value of Financial Instruments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_fcd468b8-6c42-4574-88d6-ab7c58966f0b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated year three</link:label>
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    <link:label id="lab_fbc_WholesaleDebt_6bf56f72-1cc2-4898-85ea-9a1745b4980c_totalLabel_en-US" xlink:label="lab_fbc_WholesaleDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total wholesale borrowings</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_fbc_WholesaleDebt" xlink:href="fbc-20240630.xsd#fbc_WholesaleDebt"/>
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    <link:label id="lab_fbc_FlagstarStatutoryTrustVMember_2814bdbd-0c76-4645-8c0c-c4a54d00d475_terseLabel_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust V</link:label>
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    <link:label id="lab_fbc_FlagstarStatutoryTrustVMember_documentation_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust V</link:label>
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    <link:label id="lab_us-gaap_AmortizationOfDebtDiscountPremium_811aef22-fdb6-48d0-a691-cb38e24f385f_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfDebtDiscountPremium" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of discounts and premiums, net</link:label>
    <link:label id="lab_us-gaap_AmortizationOfDebtDiscountPremium_label_en-US" xlink:label="lab_us-gaap_AmortizationOfDebtDiscountPremium" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Discount (Premium)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfDebtDiscountPremium" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AmortizationOfDebtDiscountPremium"/>
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    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PvpTableTextBlock"/>
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    <link:label id="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueWeightedAverageLife1_36a5654f-ebfa-4760-8da2-ead121c1a0b3_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueWeightedAverageLife1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average life</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_658772ee-a4eb-401f-9507-f35ee074c5b7_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalReserveBankAdvancesMember_2da77f71-99cc-4c1f-90a4-9f22909f840d_terseLabel_en-US" xlink:label="lab_us-gaap_FederalReserveBankAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal Reserve Bank term funding</link:label>
    <link:label id="lab_us-gaap_FederalReserveBankAdvancesMember_label_en-US" xlink:label="lab_us-gaap_FederalReserveBankAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Reserve Bank Advances [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalReserveBankAdvancesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalReserveBankAdvancesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalReserveBankAdvancesMember" xlink:to="lab_us-gaap_FederalReserveBankAdvancesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_b2e66e0c-69a9-4f63-babe-8e152730f79d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceInterestIncomeCashBasisMethod_d759e3a6-29b8-4410-835c-42e748ebfd55_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceInterestIncomeCashBasisMethod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-accrual loans with no related allowance - Interest Income Recognized</link:label>
    <link:label id="lab_us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceInterestIncomeCashBasisMethod_label_en-US" xlink:label="lab_us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceInterestIncomeCashBasisMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impaired Financing Receivable, with No Related Allowance, Interest Income, Cash Basis Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceInterestIncomeCashBasisMethod" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceInterestIncomeCashBasisMethod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceInterestIncomeCashBasisMethod" xlink:to="lab_us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceInterestIncomeCashBasisMethod" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_2cb430d0-cb40-4b9d-844d-2d92ef6537af_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables_8c11125c-7c84-4cdb-a142-c09c5af7727f_negatedTerseLabel_en-US" xlink:label="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of premises and equipment, net</link:label>
    <link:label id="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables_label_en-US" xlink:label="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For (Proceeds From) Other Changes In Financing Receivables</link:label>
    <link:label id="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables_documentation_en-US" xlink:label="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments For (Proceeds From) Other Changes In Financing Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:href="fbc-20240630.xsd#fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:to="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_3b04e4ee-40ca-44ec-84e3-cb9d21bb34dc_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_383b37ca-6ddd-4100-bc34-5a8bf9429ac9_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStock_7ac305f7-7614-4e85-9c79-eeaafaefffa9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on common stock</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStock" xlink:to="lab_us-gaap_DividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_cb7fe8c4-846b-41f3-a263-6269ac1e62dc_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term of contract</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseTermOfContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:to="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_61b3fd82-4da2-422e-90af-3d1d3ea8bb43_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average remaining lease term</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SeriesDPreferredStockWarrantsMember_4c8ed2f6-341e-44ec-a80c-24f9de7fa749_terseLabel_en-US" xlink:label="lab_fbc_SeriesDPreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock Warrants</link:label>
    <link:label id="lab_fbc_SeriesDPreferredStockWarrantsMember_label_en-US" xlink:label="lab_fbc_SeriesDPreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock Warrants [Member]</link:label>
    <link:label id="lab_fbc_SeriesDPreferredStockWarrantsMember_documentation_en-US" xlink:label="lab_fbc_SeriesDPreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SeriesDPreferredStockWarrantsMember" xlink:href="fbc-20240630.xsd#fbc_SeriesDPreferredStockWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_SeriesDPreferredStockWarrantsMember" xlink:to="lab_fbc_SeriesDPreferredStockWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_511e5e0d-1cb5-4eec-8c70-47d10409b943_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfStockByClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_2697346a-a631-49fa-951a-d115810a760e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_NC_545f98f5-465f-437c-8501-a0bd185923c8_terseLabel_en-US" xlink:label="lab_stpr_NC" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">North Carolina</link:label>
    <link:label id="lab_stpr_NC_label_en-US" xlink:label="lab_stpr_NC" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NORTH CAROLINA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_NC" xlink:href="https://xbrl.sec.gov/stpr/2024/stpr-2024.xsd#stpr_NC"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_NC" xlink:to="lab_stpr_NC" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
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    <link:label id="lab_fbc_NetDisbursementOfPaymentsOfLoansServicedForOthersFinancingActivities_documentation_en-US" xlink:label="lab_fbc_NetDisbursementOfPaymentsOfLoansServicedForOthersFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Disbursement Of payments Of Loans Serviced For Others, Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NetDisbursementOfPaymentsOfLoansServicedForOthersFinancingActivities" xlink:href="fbc-20240630.xsd#fbc_NetDisbursementOfPaymentsOfLoansServicedForOthersFinancingActivities"/>
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    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AdjToCompAxis"/>
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    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_509ab5ac-f96f-4589-9573-82db586bbd9d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeLiabilitiesAbstract"/>
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    <link:label id="lab_dei_DocumentQuarterlyReport_59d5a63e-f4c3-461b-ac74-3fae8402a238_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_102c66e5-689b-40de-9007-0681ab0a3990_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reclassification adjustment for net gain on cash flow hedges included in net income, net of tax of $4; $1; $10 and $3</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax"/>
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    <link:label id="lab_us-gaap_ConsumerPortfolioSegmentMember_e6253e09-bd2b-4a54-b760-2aa5c5c7dc5c_terseLabel_en-US" xlink:label="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consumer and other</link:label>
    <link:label id="lab_us-gaap_ConsumerPortfolioSegmentMember_label_en-US" xlink:label="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consumer Portfolio Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsumerPortfolioSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConsumerPortfolioSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsumerPortfolioSegmentMember" xlink:to="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_0f44d279-c491-403a-b0f7-42aa5a38e995_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from one to five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
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    <link:label id="lab_us-gaap_InterestExpenseOperating_138a1e92-7f50-4c2c-9cd6-5df6b2a26659_totalLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestExpenseOperating"/>
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    <link:label id="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock_2ad3bfe7-a69d-4b0d-913a-bbdb199ad0a1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Guarantor Obligations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Guarantor Obligations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfGuaranteeObligationsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:to="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents_512828a2-cf9c-48da-bedd-09b86baec261_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash &amp; cash equivalents</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents_label_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Cash And Cash Equivalents</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents_documentation_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Cash And Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents" xlink:href="fbc-20240630.xsd#fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents" xlink:to="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TroubledDebtRestructuringsOnFinancingReceivablesTableTextBlock_a3201b64-ae25-49ed-8105-33da686ac453_terseLabel_en-US" xlink:label="lab_us-gaap_TroubledDebtRestructuringsOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Modifications to Borrowers Experiencing Financial Difficulty and Performance of Loans Modified in Last 12 Months, and TDRs</link:label>
    <link:label id="lab_us-gaap_TroubledDebtRestructuringsOnFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_TroubledDebtRestructuringsOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Modified [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TroubledDebtRestructuringsOnFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TroubledDebtRestructuringsOnFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TroubledDebtRestructuringsOnFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_TroubledDebtRestructuringsOnFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_a0ba9c22-6d2a-4a61-873a-446447ca91a4_totalLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accumulated other comprehensive loss, net of tax</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_7020df1b-b5ac-4117-95b7-d575001ecb7e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases / Originations</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
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    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceived_5f540055-8aed-417f-927b-30075fd46924_totalLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease payments</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceived_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceived"/>
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    <link:label id="lab_us-gaap_AdvancesFromFederalHomeLoanBanks_e1c3cb06-62b4-4159-a019-b5a427e492a3_totalLabel_en-US" xlink:label="lab_us-gaap_AdvancesFromFederalHomeLoanBanks" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total FHLB advances</link:label>
    <link:label id="lab_us-gaap_AdvancesFromFederalHomeLoanBanks_label_en-US" xlink:label="lab_us-gaap_AdvancesFromFederalHomeLoanBanks" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advance from Federal Home Loan Bank</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvancesFromFederalHomeLoanBanks" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdvancesFromFederalHomeLoanBanks"/>
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    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_89149939-7281-47e1-95e6-9b6db7077d7e_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average common shares outstanding (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
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    <link:label id="lab_fbc_FlagstarStatutoryTrustXMember_5777edda-6bec-40c1-b716-5402f14d38af_terseLabel_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust X</link:label>
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    <link:label id="lab_fbc_FlagstarStatutoryTrustXMember_documentation_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust X</link:label>
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    <link:label id="lab_stpr_NY_6bae6904-304c-4050-a68e-570a70cebbbf_terseLabel_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York</link:label>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_us-gaap_ImpairedFinancingReceivableRecordedInvestment_5740f632-0584-4bf0-9084-1fcdc5bec1d5_totalLabel_en-US" xlink:label="lab_us-gaap_ImpairedFinancingReceivableRecordedInvestment" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total non-accrual loans - Recorded Investment</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_6a74e824-a17c-4ab1-a6f0-a3311d7626f6_negatedLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Forfeited (in shares)</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromLifeInsurancePolicies_2a512db5-3062-4d0b-bedf-7971e623f11a_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLifeInsurancePolicies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from bank-owned life insurance, net</link:label>
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    <link:label id="lab_fbc_LoansHeldForInvestmentMember_d400d0ad-3880-4437-b8c8-e803b57b01c3_terseLabel_en-US" xlink:label="lab_fbc_LoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held-for-investment</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_b57fc811-2cd6-402d-b012-aa7769e6dd32_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt and Equity Securities, FV-NI [Line Items]</link:label>
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    <link:label id="lab_srt_RangeMember_3003f1df-7281-40cf-9041-40e05d9333ba_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeMember"/>
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    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_ead95cf3-c01a-4e95-a506-6c9afff6606a_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Unrealized Loss</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff_0e2ae285-b72a-48c1-be56-1206d5666bee_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Originated year four</link:label>
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    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_f8ceef0f-e942-4f8e-a20e-390ca7764dfe_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Lease Cost Information</link:label>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost [Table Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCostTableTextBlock" xlink:to="lab_us-gaap_LeaseCostTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_35622ed2-2b28-446d-8435-c5b2dfeb857b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesFairValueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativesFairValueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesFairValueLineItems" xlink:to="lab_us-gaap_DerivativesFairValueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentMeasurementPeriodAdjustmentsExcludingTaxes_a37a6a77-eb4a-497b-aa1c-496512c371b3_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentMeasurementPeriodAdjustmentsExcludingTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement period adjustments, excluding taxes</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesMember_75045bea-3a91-44f4-bdec-6f8cc45cdfae_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Debt Securities:</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_5c3bcdd8-795b-449b-b4c3-e68f816a90ec_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Debt Securities Available for Sale:</link:label>
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    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_45056d63-3521-4c6d-8926-190528e20246_terseLabel_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Quality of Loans Held for Investment</link:label>
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    <link:label id="lab_fbc_SubservicingAssetatFairValueIncomeAmount_f337862d-1c29-4616-b480-e73812aad632_totalLabel_en-US" xlink:label="lab_fbc_SubservicingAssetatFairValueIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total income (loss) on mortgage loans subserviced, included in loan administration income</link:label>
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    <link:label id="lab_us-gaap_MutualFundMember_36004149-6a6e-4434-820a-c92d90c3028e_verboseLabel_en-US" xlink:label="lab_us-gaap_MutualFundMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mutual funds</link:label>
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    <link:label id="lab_srt_FinancingReceivableAllowanceForCreditLossToOutstandingPercent_6f82b652-39ac-4622-b12d-24e3284b5450_terseLabel_en-US" xlink:label="lab_srt_FinancingReceivableAllowanceForCreditLossToOutstandingPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit loss to loans held for investment ratio</link:label>
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    <link:label id="lab_fbc_PrivateLabelCMOsMember_documentation_en-US" xlink:label="lab_fbc_PrivateLabelCMOsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Label CMOs</link:label>
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    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_230db05b-c028-4b64-8a3d-6acff29d5ba6_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PassMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PassMember"/>
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    <link:label id="lab_us-gaap_CashFlowHedgingMember_3e5265df-a0e1-417c-b605-f683c0b0af61_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flow hedging</link:label>
    <link:label id="lab_us-gaap_CashFlowHedgingMember_label_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow Hedging [Member]</link:label>
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    <link:label id="lab_us-gaap_WarrantsAndRightsOutstandingTerm_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WarrantsAndRightsOutstandingTerm"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_ec3216f6-5ceb-4dc5-a575-9a7f23fee95e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross realized losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss"/>
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    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_52d87714-ca25-4194-b97d-e275fbc3f0ef_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets [Table]</link:label>
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    <link:label id="lab_us-gaap_RetirementPlanTypeAxis_a3bde135-a2f5-47e5-8890-372d836d8f70_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_TreasuryStockCommonMember_31c4cd05-8d13-4669-ac94-bc0c6f758cfb_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury Stock, at Cost</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TreasuryStockCommonMember"/>
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    <link:label id="lab_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecurities_aa3ea978-f23a-4fb9-9737-1eaaf525029c_totalLabel_en-US" xlink:label="lab_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Acquiree [Domain]</link:label>
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    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_0cce8535-9105-4716-aa05-ec2d1363061c_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
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    <link:label id="lab_fbc_ProceedsFromSaleOfDebtSecuritiesAvailableForSaleAndSecuritizedLoans_documentation_en-US" xlink:label="lab_fbc_ProceedsFromSaleOfDebtSecuritiesAvailableForSaleAndSecuritizedLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Sale Of Debt Securities, Available-For-Sale And Securitized Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ProceedsFromSaleOfDebtSecuritiesAvailableForSaleAndSecuritizedLoans" xlink:href="fbc-20240630.xsd#fbc_ProceedsFromSaleOfDebtSecuritiesAvailableForSaleAndSecuritizedLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_ProceedsFromSaleOfDebtSecuritiesAvailableForSaleAndSecuritizedLoans" xlink:to="lab_fbc_ProceedsFromSaleOfDebtSecuritiesAvailableForSaleAndSecuritizedLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_MeasurementInputOriginationPullThroughMember_81bb6e28-b39a-4aaa-b3c8-7b3bb68b6d77_terseLabel_en-US" xlink:label="lab_fbc_MeasurementInputOriginationPullThroughMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Origination pull-through rate</link:label>
    <link:label id="lab_fbc_MeasurementInputOriginationPullThroughMember_label_en-US" xlink:label="lab_fbc_MeasurementInputOriginationPullThroughMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Origination Pull-Through [Member]</link:label>
    <link:label id="lab_fbc_MeasurementInputOriginationPullThroughMember_documentation_en-US" xlink:label="lab_fbc_MeasurementInputOriginationPullThroughMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Origination - Pull Through [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_MeasurementInputOriginationPullThroughMember" xlink:href="fbc-20240630.xsd#fbc_MeasurementInputOriginationPullThroughMember"/>
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    <link:label id="lab_srt_WeightedAverageMember_8202d292-8efe-49b3-b702-bb2804c77476_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResidentialMortgageMember_2b9ddb7a-1f12-4f1b-8496-2329c389c45e_terseLabel_en-US" xlink:label="lab_us-gaap_ResidentialMortgageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential first mortgage loans</link:label>
    <link:label id="lab_us-gaap_ResidentialMortgageMember_label_en-US" xlink:label="lab_us-gaap_ResidentialMortgageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResidentialMortgageMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ResidentialMortgageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResidentialMortgageMember" xlink:to="lab_us-gaap_ResidentialMortgageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedRemainderOfFiscalYear_eb3ac54d-c5df-43d5-a551-ae80a77151b6_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedRemainderOfFiscalYear"/>
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    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_70cff1aa-4fda-4404-a22d-7d3f6be4032f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of common stock</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchasedDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
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    <link:label id="lab_us-gaap_OtherLiabilitiesMember_442b0c55-f277-4b1f-a9b6-b313a0322879_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherLiabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesMember" xlink:to="lab_us-gaap_OtherLiabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_9308620b-d178-4f00-a344-8d287367e959_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:to="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralMember_1f41c3d6-b473-4c08-b7da-3d51e291d481_terseLabel_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset pledged as collateral</link:label>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralMember_label_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Pledged as Collateral [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetPledgedAsCollateralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:to="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate_ed8b65a9-06c9-472d-963b-af72042aba21_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_f085a300-8147-4f8e-8d55-ba83dc35ff9f_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_6f91bfec-c458-4150-915d-1a93b6d69ccf_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, and restricted cash at beginning of period (1)</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_2274c922-4c1c-4516-9947-7cbb21868314_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, and restricted cash at end of period (1)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff_da722dbc-2685-4529-a0a7-185ea66863d2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Revolving Loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Revolving, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff"/>
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    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_f70bb27e-96be-424d-afd7-ada6e1a4155e_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity investments with readily determinable fair values, at fair value</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_f0a7a7ca-d5ce-4472-ad57-5bfb721905fb_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNi" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquitySecuritiesFvNi"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNi" xlink:to="lab_us-gaap_EquitySecuritiesFvNi" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_BusinessCombinationSettlementProcessPeriod_e17ca1e4-f25b-484d-9a2d-fc72c36fbaec_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationSettlementProcessPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Settlement period</link:label>
    <link:label id="lab_fbc_BusinessCombinationSettlementProcessPeriod_label_en-US" xlink:label="lab_fbc_BusinessCombinationSettlementProcessPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Settlement Process Period</link:label>
    <link:label id="lab_fbc_BusinessCombinationSettlementProcessPeriod_documentation_en-US" xlink:label="lab_fbc_BusinessCombinationSettlementProcessPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Settlement Process Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BusinessCombinationSettlementProcessPeriod" xlink:href="fbc-20240630.xsd#fbc_BusinessCombinationSettlementProcessPeriod"/>
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    <link:label id="lab_us-gaap_RisksInherentInServicingAssetsAndServicingLiabilitiesTypeDomain_c9844cf5-5cdb-4fca-bcdf-478923462fc3_terseLabel_en-US" xlink:label="lab_us-gaap_RisksInherentInServicingAssetsAndServicingLiabilitiesTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risks Inherent in Servicing Assets and Servicing Liabilities, Type [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RisksInherentInServicingAssetsAndServicingLiabilitiesTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RisksInherentInServicingAssetsAndServicingLiabilitiesTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RisksInherentInServicingAssetsAndServicingLiabilitiesTypeDomain" xlink:to="lab_us-gaap_RisksInherentInServicingAssetsAndServicingLiabilitiesTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquityDividendRatePercentage_a160d4f9-402b-44ad-a4ff-cfbabf461ef9_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend rate percentage</link:label>
    <link:label id="lab_fbc_TemporaryEquityDividendRatePercentage_label_en-US" xlink:label="lab_fbc_TemporaryEquityDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Dividend Rate, Percentage</link:label>
    <link:label id="lab_fbc_TemporaryEquityDividendRatePercentage_documentation_en-US" xlink:label="lab_fbc_TemporaryEquityDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquityDividendRatePercentage" xlink:href="fbc-20240630.xsd#fbc_TemporaryEquityDividendRatePercentage"/>
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    <link:label id="lab_us-gaap_TreasuryStockCommonShares_10f43a9b-0a68-4833-ab00-eaa06acedabb_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonShares" xlink:to="lab_us-gaap_TreasuryStockCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SeriesDNYCEStockMember_994ea112-e183-4cc6-aa8f-818153f690dd_terseLabel_en-US" xlink:label="lab_fbc_SeriesDNYCEStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series D NYCE Stock</link:label>
    <link:label id="lab_fbc_SeriesDNYCEStockMember_label_en-US" xlink:label="lab_fbc_SeriesDNYCEStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D NYCE Stock [Member]</link:label>
    <link:label id="lab_fbc_SeriesDNYCEStockMember_documentation_en-US" xlink:label="lab_fbc_SeriesDNYCEStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series D NYCE Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SeriesDNYCEStockMember" xlink:href="fbc-20240630.xsd#fbc_SeriesDNYCEStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_SeriesDNYCEStockMember" xlink:to="lab_fbc_SeriesDNYCEStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears_2312f8ac-0625-412a-9298-9cd6a87f5106_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:to="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateTwoToThreeYearsFromBalanceSheetDate_f143a298-1f1a-4c50-bd56-0a2de8e0d979_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateTwoToThreeYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateTwoToThreeYearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateTwoToThreeYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Average Interest Rate, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateTwoToThreeYearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateTwoToThreeYearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateTwoToThreeYearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateTwoToThreeYearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_cff7ad08-3da8-4ae6-b9ad-ae866fe3362e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment_e748f4b4-b644-4be0-a1dd-d6e14bfd73b0_negatedTerseLabel_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: purchase accounting adjustment</link:label>
    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment_label_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-type and Direct Financing Leases, Lease Receivable, Purchase Accounting Adjustment</link:label>
    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment_documentation_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sales-type and Direct Financing Leases, Lease Receivable, Purchase Accounting Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:href="fbc-20240630.xsd#fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:to="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1_759fd360-b9ed-445d-aaf6-649c1c231474_terseLabel_en-US" xlink:label="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term of lease</link:label>
    <link:label id="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1_label_en-US" xlink:label="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Direct Financing Lease, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LessorDirectFinancingLeaseTermOfContract1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:to="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_a0b5ae85-27f9-4a87-aebf-566fb05c4b33_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingAbstract_5bf95de8-2e69-4ec0-8397-dc9d04bd7c16_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers and Servicing [Abstract]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingAbstract_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfers and Servicing [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingAbstract" xlink:to="lab_us-gaap_TransfersAndServicingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_c8148b21-21fb-4f64-8239-3f9d9abbb5ea_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_31ddfe84-70e0-4c07-b46f-f84837e0cca3_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable rate on spread</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_734abad5-7844-49a9-a85a-e1350809f73e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember_bfa67b0a-f2d3-4aa0-b457-59794990b3bb_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification from AOCI</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_25fd9e69-fcad-4859-bcf3-2b26ba22133c_terseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation and benefits</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_label_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor and Related Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LaborAndRelatedExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LaborAndRelatedExpense" xlink:to="lab_us-gaap_LaborAndRelatedExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember_92b6cb63-55b6-4cb7-b77e-562030c3437c_terseLabel_en-US" xlink:label="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed To Floating Rate Series A Noncumulative Perpetual Preferred Stock</link:label>
    <link:label id="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember_label_en-US" xlink:label="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed To Floating Rate Series A Noncumulative Perpetual Preferred Stock [Member]</link:label>
    <link:label id="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember_documentation_en-US" xlink:label="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed to floating rate series A noncumulative perpetual preferred stock.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember" xlink:href="fbc-20240630.xsd#fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember" xlink:to="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitment_8c2a8415-5c5c-4fe0-98f3-2ad4bfb9b765_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total loan commitments</link:label>
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    <link:label id="lab_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue_48faf94b-7b03-4862-9789-9c37bfc0f5be_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Decrease in MSR fair value due to pay-offs, pay-downs, run-off, model changes and other</link:label>
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    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
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    <link:label id="lab_us-gaap_OtherAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets [Member]</link:label>
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    <link:label id="lab_us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment_ecc69a53-e0a7-4708-a673-408613bb6128_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-accrual loans with no related allowance - Recorded Investment</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss_e339b8ef-eecf-4168-a1a5-1f6636c5de07_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Unrealized Loss</link:label>
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    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherAssets_14166ec3-4c73-432e-be02-6b2a61a5c7e9_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock_44f7dcad-d422-4177-81d8-5cda07d266e9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Federal Home Loan Bank, Advances, by Branch of FHLB Bank</link:label>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRateMaturingInRollingYearFive_ca7aba5a-6e48-41ed-b1a5-a5f02af022d0_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRateMaturingInRollingYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_8e4b97fc-38a7-4978-9141-996cbd03bfda_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring [Member]</link:label>
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    <link:label id="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis_2127b4b5-f1b1-4d2d-9fc1-3bceed4c335a_terseLabel_en-US" xlink:label="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Conversion Description [Axis]</link:label>
    <link:label id="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis_label_en-US" xlink:label="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Conversion Description [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConversionOfStockByUniqueDescriptionAxis"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_b21a7029-db47-463d-9924-10fda78410bb_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
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    <link:label id="lab_fbc_FinancingReceivableAllowanceForCreditLossRepriceDuringPeriod_613bb6fa-58b6-42d6-be26-524c07802d79_terseLabel_en-US" xlink:label="lab_fbc_FinancingReceivableAllowanceForCreditLossRepriceDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit loss, reprice period</link:label>
    <link:label id="lab_fbc_FinancingReceivableAllowanceForCreditLossRepriceDuringPeriod_label_en-US" xlink:label="lab_fbc_FinancingReceivableAllowanceForCreditLossRepriceDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Reprice During Period</link:label>
    <link:label id="lab_fbc_FinancingReceivableAllowanceForCreditLossRepriceDuringPeriod_documentation_en-US" xlink:label="lab_fbc_FinancingReceivableAllowanceForCreditLossRepriceDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Reprice During Period</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_3d095d7d-a846-478e-a5ca-25d45f671281_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Twelve Months or Longer, Fair Value</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_8b65028a-51e7-4f6b-9a99-517506f97881_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in other miscellaneous liabilities</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax_fcee75b3-53f6-4b08-b9a1-198c294fe26f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in net unrealized gain on cash flow hedges, tax</link:label>
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    <link:label id="lab_us-gaap_LongTermDebt_548c66c9-4831-4cd6-9ea7-2cdf67238b35_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total borrowed funds</link:label>
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    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
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    <link:label id="lab_fbc_FairValueOptionContractualPrincipalOutstandingAssets_554190dd-2897-49fa-90dc-907de8087bd7_terseLabel_en-US" xlink:label="lab_fbc_FairValueOptionContractualPrincipalOutstandingAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unpaid Principal Balance</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_f8693cfa-1467-476c-98dc-134b65e4279b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and leases held for investment, net of deferred loan fees and costs ($68 and zero measured at fair value at June&#160;30, 2024 and December&#160;31, 2023, respectively)</link:label>
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    <link:label id="lab_fbc_AssetsAndLiabilitiesLesseeTableTextBlock_df363100-f224-4a92-a961-a769c2fc8caa_terseLabel_en-US" xlink:label="lab_fbc_AssetsAndLiabilitiesLesseeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Supplemental Balance Sheet Information</link:label>
    <link:label id="lab_fbc_AssetsAndLiabilitiesLesseeTableTextBlock_label_en-US" xlink:label="lab_fbc_AssetsAndLiabilitiesLesseeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets And Liabilities, Lessee [Table Text Block]</link:label>
    <link:label id="lab_fbc_AssetsAndLiabilitiesLesseeTableTextBlock_documentation_en-US" xlink:label="lab_fbc_AssetsAndLiabilitiesLesseeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets And Liabilities, Lessee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_AssetsAndLiabilitiesLesseeTableTextBlock" xlink:href="fbc-20240630.xsd#fbc_AssetsAndLiabilitiesLesseeTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_AssetsAndLiabilitiesLesseeTableTextBlock" xlink:to="lab_fbc_AssetsAndLiabilitiesLesseeTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_7c9e1164-2a97-4c76-8014-29c830ce1861_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:to="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_LineOfCreditFacilityAdvancesLockOutPeriod_8d270d9b-7ad6-4836-80ad-bd27030e6238_terseLabel_en-US" xlink:label="lab_fbc_LineOfCreditFacilityAdvancesLockOutPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FHLB lockout period</link:label>
    <link:label id="lab_fbc_LineOfCreditFacilityAdvancesLockOutPeriod_label_en-US" xlink:label="lab_fbc_LineOfCreditFacilityAdvancesLockOutPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Advances Lock Out Period</link:label>
    <link:label id="lab_fbc_LineOfCreditFacilityAdvancesLockOutPeriod_documentation_en-US" xlink:label="lab_fbc_LineOfCreditFacilityAdvancesLockOutPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Advances Lock Out Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_LineOfCreditFacilityAdvancesLockOutPeriod" xlink:href="fbc-20240630.xsd#fbc_LineOfCreditFacilityAdvancesLockOutPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_LineOfCreditFacilityAdvancesLockOutPeriod" xlink:to="lab_fbc_LineOfCreditFacilityAdvancesLockOutPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseLongTermDebt_bdf9c541-811e-4165-b759-69efa8ca0f61_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowed funds</link:label>
    <link:label id="lab_us-gaap_InterestExpenseLongTermDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestExpenseLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseLongTermDebt" xlink:to="lab_us-gaap_InterestExpenseLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableSale_d6892dfc-3883-413f-bf01-65b6ee838363_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing receivable, sale</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableSale_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableSale" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableSale" xlink:to="lab_us-gaap_FinancingReceivableSale" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis_03b256dc-0afc-4a3f-9be1-78009a586baa_terseLabel_en-US" xlink:label="lab_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank Branch [Axis]</link:label>
    <link:label id="lab_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis_label_en-US" xlink:label="lab_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank Branch [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis" xlink:to="lab_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_9721a68a-e5a5-454a-b92b-b33665557067_verboseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Intangible asset amortization</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_ffb6ce0e-1e5b-4de0-bfcf-312aebfd7708_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of intangibles</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityAbstract_e79a1935-2451-46fa-b707-8f9985a8fef1_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mezzanine equity:</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityAbstract_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityAbstract" xlink:to="lab_us-gaap_TemporaryEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset_036d6cfe-e050-450a-a948-f4f16f7e6261_terseLabel_en-US" xlink:label="lab_us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment in the lease - unguaranteed residual assets</link:label>
    <link:label id="lab_us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset_label_en-US" xlink:label="lab_us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Financing Lease, Unguaranteed Residual Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset" xlink:to="lab_us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax_bcbe7d57-5f85-442e-89cb-921d74218105_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification adjustment for defined benefit pension plan, net of tax of $0; $1; $0 and $0</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_68f5dcb0-d821-4d06-8567-d066615b4902_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends, Income Statement Impact</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockDividendsIncomeStatementImpact"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:to="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SensitivityAnalysisActualAbstract_9e1b2202-515a-4766-9894-0304dc1710e9_terseLabel_en-US" xlink:label="lab_fbc_SensitivityAnalysisActualAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Actual</link:label>
    <link:label id="lab_fbc_SensitivityAnalysisActualAbstract_label_en-US" xlink:label="lab_fbc_SensitivityAnalysisActualAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sensitivity Analysis, Actual [Abstract]</link:label>
    <link:label id="lab_fbc_SensitivityAnalysisActualAbstract_documentation_en-US" xlink:label="lab_fbc_SensitivityAnalysisActualAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sensitivity Analysis, Actual [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SensitivityAnalysisActualAbstract" xlink:href="fbc-20240630.xsd#fbc_SensitivityAnalysisActualAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_SensitivityAnalysisActualAbstract" xlink:to="lab_fbc_SensitivityAnalysisActualAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_15d15f06-89c2-4fc4-b3b3-f3cfac2da12b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:to="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_4e3fdaf8-0951-492e-a2cb-f1374013c603_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combinations</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:to="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_e1352f33-02f7-4a10-b5b8-da202576f933_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateLockCommitmentsMember_53ea100d-7633-47af-a4fd-6faf330d62d0_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateLockCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rate lock commitments</link:label>
    <link:label id="lab_us-gaap_InterestRateLockCommitmentsMember_label_en-US" xlink:label="lab_us-gaap_InterestRateLockCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Lock Commitments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateLockCommitmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestRateLockCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateLockCommitmentsMember" xlink:to="lab_us-gaap_InterestRateLockCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_ce74aa5f-c8f7-4373-b059-8125c0dcd317_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: imputed interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
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    <link:label id="lab_fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour_7ffc9eae-d7a5-44e3-a8a6-86cab821fb98_terseLabel_en-US" xlink:label="lab_fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour_label_en-US" xlink:label="lab_fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Due after Year Four</link:label>
    <link:label id="lab_fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour_documentation_en-US" xlink:label="lab_fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Due after Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour" xlink:href="fbc-20240630.xsd#fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour" xlink:to="lab_fbc_LesseeOperatingLeaseLiabilityToBePaidDueAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NoncumulativeConvertiblePreferredStockSeriesCMember_d09c1589-6722-4203-ae67-329644da8b26_terseLabel_en-US" xlink:label="lab_fbc_NoncumulativeConvertiblePreferredStockSeriesCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncumulative Convertible Preferred Stock Series C</link:label>
    <link:label id="lab_fbc_NoncumulativeConvertiblePreferredStockSeriesCMember_label_en-US" xlink:label="lab_fbc_NoncumulativeConvertiblePreferredStockSeriesCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncumulative Convertible Preferred Stock Series C [Member]</link:label>
    <link:label id="lab_fbc_NoncumulativeConvertiblePreferredStockSeriesCMember_documentation_en-US" xlink:label="lab_fbc_NoncumulativeConvertiblePreferredStockSeriesCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncumulative Convertible Preferred Stock Series C</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NoncumulativeConvertiblePreferredStockSeriesCMember" xlink:href="fbc-20240630.xsd#fbc_NoncumulativeConvertiblePreferredStockSeriesCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NoncumulativeConvertiblePreferredStockSeriesCMember" xlink:to="lab_fbc_NoncumulativeConvertiblePreferredStockSeriesCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermInvestments_bf883e73-56f1-409f-aac1-146e1b90b735_totalLabel_en-US" xlink:label="lab_us-gaap_ShortTermInvestments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total securities net of allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_ShortTermInvestments_label_en-US" xlink:label="lab_us-gaap_ShortTermInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortTermInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermInvestments" xlink:to="lab_us-gaap_ShortTermInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TimeDeposits_444c7cd8-7806-428f-b430-c7f56544f46f_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Certificates of deposit</link:label>
    <link:label id="lab_us-gaap_TimeDeposits_label_en-US" xlink:label="lab_us-gaap_TimeDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TimeDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TimeDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TimeDeposits" xlink:to="lab_us-gaap_TimeDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankStock_e60ce89e-411d-4829-a793-749b00690529_verboseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankStock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank stock and Federal Reserve Bank stock, at cost</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankStock_3a06ddd3-d626-41a7-85d0-16dbd4f72d48_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal home loan bank stock</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankStock_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalHomeLoanBankStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalHomeLoanBankStock" xlink:to="lab_us-gaap_FederalHomeLoanBankStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VestingAxis_881da27f-11a6-4c04-856f-2a3c6d9ff11d_terseLabel_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:label id="lab_us-gaap_VestingAxis_label_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VestingAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingAxis" xlink:to="lab_us-gaap_VestingAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_a29de0c8-4a82-4ee6-adce-b24719f9a698_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoanRestructuringModificationDomain_97ec036e-efa0-4ac8-8fc3-3add0bed5bf5_terseLabel_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:label id="lab_us-gaap_LoanRestructuringModificationDomain_label_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoanRestructuringModificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LoanRestructuringModificationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoanRestructuringModificationDomain" xlink:to="lab_us-gaap_LoanRestructuringModificationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_ForeignNotesMember_9f7949e2-c616-4ddf-ad8b-b51ab39e06cf_terseLabel_en-US" xlink:label="lab_fbc_ForeignNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign notes</link:label>
    <link:label id="lab_fbc_ForeignNotesMember_label_en-US" xlink:label="lab_fbc_ForeignNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Notes [Member]</link:label>
    <link:label id="lab_fbc_ForeignNotesMember_documentation_en-US" xlink:label="lab_fbc_ForeignNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Foreign Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ForeignNotesMember" xlink:href="fbc-20240630.xsd#fbc_ForeignNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_ForeignNotesMember" xlink:to="lab_fbc_ForeignNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_244f4462-f251-41a4-b611-28f29b48db42_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash &amp; cash equivalents</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Cash and Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentIntangibles_01b7fb57-c020-4070-86ec-6c5114ca3368_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentIntangibles" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Core deposit and other intangibles</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentIntangibles_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentIntangibles" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Intangibles</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentIntangibles" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentIntangibles"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentIntangibles" xlink:to="lab_us-gaap_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentIntangibles" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustXMember_c23ca5c7-3ff3-46a8-bb0a-d968e8030d38_terseLabel_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust X</link:label>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustXMember_label_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust X [Member]</link:label>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustXMember_documentation_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust X</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NewYorkCommunityCapitalTrustXMember" xlink:href="fbc-20240630.xsd#fbc_NewYorkCommunityCapitalTrustXMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NewYorkCommunityCapitalTrustXMember" xlink:to="lab_fbc_NewYorkCommunityCapitalTrustXMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementAxis_a2426962-170a-4f2a-925a-a6105fb56aad_terseLabel_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Axis]</link:label>
    <link:label id="lab_srt_RestatementAxis_label_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RestatementAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementAxis" xlink:to="lab_srt_RestatementAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_629fb903-032c-447d-9922-e543ffeb689b_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets acquired</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets"/>
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    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_e25d499d-ead9-4266-87ba-bf9a58f14ade_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_ResidentialMortgageServicingBusinessMember_ba803d13-0228-4a3b-b4ef-f16e36d179ad_terseLabel_en-US" xlink:label="lab_fbc_ResidentialMortgageServicingBusinessMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential Mortgage Servicing Business</link:label>
    <link:label id="lab_fbc_ResidentialMortgageServicingBusinessMember_label_en-US" xlink:label="lab_fbc_ResidentialMortgageServicingBusinessMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Servicing Business [Member]</link:label>
    <link:label id="lab_fbc_ResidentialMortgageServicingBusinessMember_documentation_en-US" xlink:label="lab_fbc_ResidentialMortgageServicingBusinessMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Mortgage Servicing Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ResidentialMortgageServicingBusinessMember" xlink:href="fbc-20240630.xsd#fbc_ResidentialMortgageServicingBusinessMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_ResidentialMortgageServicingBusinessMember" xlink:to="lab_fbc_ResidentialMortgageServicingBusinessMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_9763256a-50e4-404c-813d-d30ac5ecfb2a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxesPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaid" xlink:to="lab_us-gaap_IncomeTaxesPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_CommercialRealEstateLoansMember_7d489e18-0f71-4f17-915e-465952910a6a_terseLabel_en-US" xlink:label="lab_fbc_CommercialRealEstateLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial real estate</link:label>
    <link:label id="lab_fbc_CommercialRealEstateLoansMember_label_en-US" xlink:label="lab_fbc_CommercialRealEstateLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Real Estate Loans [Member]</link:label>
    <link:label id="lab_fbc_CommercialRealEstateLoansMember_documentation_en-US" xlink:label="lab_fbc_CommercialRealEstateLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Portfolio segment of the company's total financing receivables related to commercial real estate loans that are collateralized by real estate properties intended to be income-producing in the normal course of business.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_CommercialRealEstateLoansMember" xlink:href="fbc-20240630.xsd#fbc_CommercialRealEstateLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_CommercialRealEstateLoansMember" xlink:to="lab_fbc_CommercialRealEstateLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_d94e65d9-a807-4c3c-be4c-0a0f6e202882_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financial Instruments Carried at Fair Value</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralizedMortgageObligationsMember_6f25d4ce-66bf-4488-90ef-071808be136f_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralizedMortgageObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GSE collateralized mortgage obligations</link:label>
    <link:label id="lab_us-gaap_CollateralizedMortgageObligationsMember_label_en-US" xlink:label="lab_us-gaap_CollateralizedMortgageObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Mortgage Obligations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralizedMortgageObligationsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CollateralizedMortgageObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralizedMortgageObligationsMember" xlink:to="lab_us-gaap_CollateralizedMortgageObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_ac2431af-d7b7-4c60-8695-43f21ad3c0a6_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_CommonStockLiquidationPreferenceValue_87fa3f17-1729-427c-b2db-8b902d0ae376_terseLabel_en-US" xlink:label="lab_fbc_CommonStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_fbc_CommonStockLiquidationPreferenceValue_label_en-US" xlink:label="lab_fbc_CommonStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Liquidation Preference, Value</link:label>
    <link:label id="lab_fbc_CommonStockLiquidationPreferenceValue_documentation_en-US" xlink:label="lab_fbc_CommonStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Liquidation Preference, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_CommonStockLiquidationPreferenceValue" xlink:href="fbc-20240630.xsd#fbc_CommonStockLiquidationPreferenceValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_CommonStockLiquidationPreferenceValue" xlink:to="lab_fbc_CommonStockLiquidationPreferenceValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromTwoToThreeYearsOfBalanceSheetDate_18d2e540-c024-4c59-8274-36b38ca1e10a_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromTwoToThreeYearsOfBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromTwoToThreeYearsOfBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromTwoToThreeYearsOfBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromTwoToThreeYearsOfBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromTwoToThreeYearsOfBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromTwoToThreeYearsOfBalanceSheetDate" xlink:to="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueFromTwoToThreeYearsOfBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SignatureBridgeBankMember_3bbac5f7-4183-4ff7-a9a7-d83adc147cda_terseLabel_en-US" xlink:label="lab_fbc_SignatureBridgeBankMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Signature Bridge Bank</link:label>
    <link:label id="lab_fbc_SignatureBridgeBankMember_label_en-US" xlink:label="lab_fbc_SignatureBridgeBankMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Signature Bridge Bank [Member]</link:label>
    <link:label id="lab_fbc_SignatureBridgeBankMember_documentation_en-US" xlink:label="lab_fbc_SignatureBridgeBankMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Signature Bridge Bank</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SignatureBridgeBankMember" xlink:href="fbc-20240630.xsd#fbc_SignatureBridgeBankMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_SignatureBridgeBankMember" xlink:to="lab_fbc_SignatureBridgeBankMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_70eba31b-9703-4329-9b6b-1bd4c62219b9_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based payment arrangement, tranche two</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Tranche Two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationAwardTrancheTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:to="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember_cf7b967a-5f1b-459c-b41a-e755e1d0c296_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Defined Benefit Plans Adjustment Attributable to Parent</link:label>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Defined Benefit Plans Adjustment Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember" xlink:to="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_42ce7757-631f-442a-affa-f642d6844d55_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate of Capital Securities and Debentures</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_7cac4de0-868b-4bc7-86f5-a5f4f2cceeb0_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate at June 30, 2024</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsLineItems_a7efb793-0b83-47b7-bdd7-f779abd8fab1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued_2b8a5d15-8f6e-4eff-ba48-332c646681bd_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of warrants to purchase common shares</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Additional Paid in Capital, Warrant Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_d91b6bee-141a-4b4b-9153-401cf95d8de9_verboseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Supplemental information:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankStateDomain_4588eb09-af2e-42ff-87ee-da9d6e42f26c_terseLabel_en-US" xlink:label="lab_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankStateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank Branch [Domain]</link:label>
    <link:label id="lab_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankStateDomain_label_en-US" xlink:label="lab_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankStateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank Branch [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankStateDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankStateDomain"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_c503fa17-8358-4841-b885-92284e3981fa_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Fair value of net identifiable assets</link:label>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesLongTerm_5cd296d4-6be6-4091-a3d4-110186a2404c_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesLongTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank and Federal Reserve Bank advances</link:label>
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    <link:label id="lab_us-gaap_LoansHeldForSaleFairValueDisclosure_65f6ce1f-6768-4903-a0fb-6958ffa99bb4_verboseLabel_en-US" xlink:label="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loans held-for-sale, fair value</link:label>
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    <link:label id="lab_fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount_bbcd7944-4948-4720-aafc-58d65d8f9fe0_negatedTerseLabel_en-US" xlink:label="lab_fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other servicing charges</link:label>
    <link:label id="lab_fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount_label_en-US" xlink:label="lab_fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Servicing Charges Generated by Servicing Financial Assets, Amount</link:label>
    <link:label id="lab_fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount_documentation_en-US" xlink:label="lab_fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The total amount of other servicing charges earned on loans serviced and subserviced for others during the period for which results of operations are presented.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount" xlink:href="fbc-20240630.xsd#fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount" xlink:to="lab_fbc_OtherServicingChargesGeneratedbyServicingFinancialAssetsAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateSwaptionMember_e3e05075-2c22-4796-aa49-d0fa3e4abb2b_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwaptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaptions</link:label>
    <link:label id="lab_us-gaap_InterestRateSwaptionMember_label_en-US" xlink:label="lab_us-gaap_InterestRateSwaptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swaption [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateSwaptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestRateSwaptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateSwaptionMember" xlink:to="lab_us-gaap_InterestRateSwaptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorDirectFinancingLeasesTextBlock_dc0a8076-cb54-4f32-bd66-91ad577a03a8_terseLabel_en-US" xlink:label="lab_us-gaap_LessorDirectFinancingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LessorDirectFinancingLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LessorDirectFinancingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Direct Financing Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorDirectFinancingLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LessorDirectFinancingLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorDirectFinancingLeasesTextBlock" xlink:to="lab_us-gaap_LessorDirectFinancingLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract_6ec8e619-264f-41b1-aafd-734717d66696_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation Preference</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract_label_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Liquidation Preference [Abstract]</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract_documentation_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Liquidation Preference</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:href="fbc-20240630.xsd#fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:to="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NonaccrualLoansMember_c94041a8-1cfa-4697-9004-2bb79ecc4dfd_terseLabel_en-US" xlink:label="lab_fbc_NonaccrualLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-accrual loans:</link:label>
    <link:label id="lab_fbc_NonaccrualLoansMember_label_en-US" xlink:label="lab_fbc_NonaccrualLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonaccrual Loans [Member]</link:label>
    <link:label id="lab_fbc_NonaccrualLoansMember_documentation_en-US" xlink:label="lab_fbc_NonaccrualLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Nonaccrual Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NonaccrualLoansMember" xlink:href="fbc-20240630.xsd#fbc_NonaccrualLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NonaccrualLoansMember" xlink:to="lab_fbc_NonaccrualLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_CommercialAndIndustrialLoansMember_a507caca-7a09-4885-ab93-d5f3c8e94578_terseLabel_en-US" xlink:label="lab_fbc_CommercialAndIndustrialLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial and industrial</link:label>
    <link:label id="lab_fbc_CommercialAndIndustrialLoansMember_label_en-US" xlink:label="lab_fbc_CommercialAndIndustrialLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial and Industrial Loans [Member]</link:label>
    <link:label id="lab_fbc_CommercialAndIndustrialLoansMember_documentation_en-US" xlink:label="lab_fbc_CommercialAndIndustrialLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Portfolio segment of the company's total financing receivables related to commercial and industrial loans, which includes lines of credit to small or middle market businesses for use in normal business operations to finance working capital needs, equipment purchases and expansion projects.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_CommercialAndIndustrialLoansMember" xlink:href="fbc-20240630.xsd#fbc_CommercialAndIndustrialLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_CommercialAndIndustrialLoansMember" xlink:to="lab_fbc_CommercialAndIndustrialLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateThreeToFourYearsFromBalanceSheetDate_d781e7bd-4dc6-41ee-8665-a86777a9343d_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateThreeToFourYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateThreeToFourYearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateThreeToFourYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Average Interest Rate, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateThreeToFourYearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateThreeToFourYearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateThreeToFourYearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateThreeToFourYearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_b4208fe3-00dc-407b-90cd-b814e29268cc_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted_7b86bc90-02a8-4c7a-9b76-7c321bd6b77e_totalLabel_en-US" xlink:label="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total commitments</link:label>
    <link:label id="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted_label_en-US" xlink:label="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments And Guarantor Obligations, Maximum Exposure, Undiscounted</link:label>
    <link:label id="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted_documentation_en-US" xlink:label="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Commitments And Guarantor Obligations, Maximum Exposure, Undiscounted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:href="fbc-20240630.xsd#fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:to="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_PrivateCollateralizedMortgageObligationsMember_16bc8c23-5145-4ac4-a288-43487cabafcd_terseLabel_en-US" xlink:label="lab_fbc_PrivateCollateralizedMortgageObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Collateralized Mortgage Obligations</link:label>
    <link:label id="lab_fbc_PrivateCollateralizedMortgageObligationsMember_label_en-US" xlink:label="lab_fbc_PrivateCollateralizedMortgageObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Collateralized Mortgage Obligations [Member]</link:label>
    <link:label id="lab_fbc_PrivateCollateralizedMortgageObligationsMember_documentation_en-US" xlink:label="lab_fbc_PrivateCollateralizedMortgageObligationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Collateralized Mortgage Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_PrivateCollateralizedMortgageObligationsMember" xlink:href="fbc-20240630.xsd#fbc_PrivateCollateralizedMortgageObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_PrivateCollateralizedMortgageObligationsMember" xlink:to="lab_fbc_PrivateCollateralizedMortgageObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember_9492082c-1f75-408b-a2a0-53bcaf26275d_terseLabel_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust V (BONUSES Units)</link:label>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember_label_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust V (BONUSES Units) [Member]</link:label>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember_documentation_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust V (BONUSES Units)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:href="fbc-20240630.xsd#fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:to="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_ServicingAssetatFairValueNetTransactionCosts_846365a9-9953-4568-861e-8118d1ab13d2_terseLabel_en-US" xlink:label="lab_fbc_ServicingAssetatFairValueNetTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net transaction costs</link:label>
    <link:label id="lab_fbc_ServicingAssetatFairValueNetTransactionCosts_label_en-US" xlink:label="lab_fbc_ServicingAssetatFairValueNetTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Net Transaction Costs</link:label>
    <link:label id="lab_fbc_ServicingAssetatFairValueNetTransactionCosts_documentation_en-US" xlink:label="lab_fbc_ServicingAssetatFairValueNetTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The total amount of net transaction costs earned on loans serviced and subserviced for others during the period for which results of operations are presented.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ServicingAssetatFairValueNetTransactionCosts" xlink:href="fbc-20240630.xsd#fbc_ServicingAssetatFairValueNetTransactionCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_ServicingAssetatFairValueNetTransactionCosts" xlink:to="lab_fbc_ServicingAssetatFairValueNetTransactionCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock_404e8eff-4bf6-4ad0-b3e6-f959d3aa1d37_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow Hedges Included in Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow Hedges Included in Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_6ced269d-9ac6-4460-a7ff-69c63253f25b_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' equity:</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityAbstract" xlink:to="lab_us-gaap_StockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_4d77247a-c1bb-4903-b4c1-7b90d4afc1ad_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than Twelve Months, Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_42289052-17bf-42a9-a686-2e018a5d8ece_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NON-INTEREST INCOME:</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoninterestIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeAbstract" xlink:to="lab_us-gaap_NoninterestIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExtendedMaturityMember_d04ce41e-0250-43e1-858e-ecad9e556268_terseLabel_en-US" xlink:label="lab_us-gaap_ExtendedMaturityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Extension</link:label>
    <link:label id="lab_us-gaap_ExtendedMaturityMember_label_en-US" xlink:label="lab_us-gaap_ExtendedMaturityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extended Maturity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExtendedMaturityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ExtendedMaturityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExtendedMaturityMember" xlink:to="lab_us-gaap_ExtendedMaturityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearThree_fc3e4f1a-0a5c-40b6-9d17-c2ca06d8bf91_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearThree_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advances, Earlier of Contractual Maturity or Next Put or Convert Date, in Rolling Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearThree" xlink:to="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateInRollingYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_9e83d5a2-0bcd-456d-8755-e1022f2a5bd5_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExtendedMaturityAndInterestRateReductionMember_4fdbafe8-c009-4f24-8909-9b418bd77a8c_terseLabel_en-US" xlink:label="lab_us-gaap_ExtendedMaturityAndInterestRateReductionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Combination - Interest Rate Reduction &amp; Term Extension</link:label>
    <link:label id="lab_us-gaap_ExtendedMaturityAndInterestRateReductionMember_label_en-US" xlink:label="lab_us-gaap_ExtendedMaturityAndInterestRateReductionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extended Maturity and Interest Rate Reduction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExtendedMaturityAndInterestRateReductionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ExtendedMaturityAndInterestRateReductionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExtendedMaturityAndInterestRateReductionMember" xlink:to="lab_us-gaap_ExtendedMaturityAndInterestRateReductionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityLineItems_b768b490-fdac-4d7e-a30d-6d53722b3682_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity [Line Items]</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLineItems_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLineItems" xlink:to="lab_us-gaap_TemporaryEquityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnOilAndGasHedgingActivity_17178e2e-5dd4-4a2d-8f62-f04af501b478_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on MSR derivatives</link:label>
    <link:label id="lab_us-gaap_GainLossOnOilAndGasHedgingActivity_label_en-US" xlink:label="lab_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Hedging Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainLossOnOilAndGasHedgingActivity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:to="lab_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NetLoanAdministrationIncomeMember_da9f4495-37f2-4f9e-8531-22b652bd89ec_terseLabel_en-US" xlink:label="lab_fbc_NetLoanAdministrationIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan administration income on mortgage loans subserviced</link:label>
    <link:label id="lab_fbc_NetLoanAdministrationIncomeMember_label_en-US" xlink:label="lab_fbc_NetLoanAdministrationIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Loan Administration Income [Member]</link:label>
    <link:label id="lab_fbc_NetLoanAdministrationIncomeMember_documentation_en-US" xlink:label="lab_fbc_NetLoanAdministrationIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the net loan administration income.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NetLoanAdministrationIncomeMember" xlink:href="fbc-20240630.xsd#fbc_NetLoanAdministrationIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NetLoanAdministrationIncomeMember" xlink:to="lab_fbc_NetLoanAdministrationIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember_48e4812c-6dcf-4870-a64a-373d1499e751_terseLabel_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other non-interest income</link:label>
    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember_label_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income, Other Operating Income [Member]</link:label>
    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember_documentation_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents other forms of revenue earned, excluding interest, which is not otherwise specified in the taxonomy.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:href="fbc-20240630.xsd#fbc_NoninterestIncomeOtherOperatingIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:to="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralTable_386a733b-8ca6-44a7-af35-586f7d5ce605_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments Owned and Pledged as Collateral [Table]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralTable_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments Owned and Pledged as Collateral [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralTable" xlink:to="lab_us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_16a44493-0c08-4cb2-9864-eb46ce5b730f_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total loans and leases held for investment, net</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember_351f6daa-f4a0-4986-be17-e3aee0621eb9_terseLabel_en-US" xlink:label="lab_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post- Retirement Benefits</link:label>
    <link:label id="lab_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember_label_en-US" xlink:label="lab_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Postretirement Benefits Plan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember" xlink:to="lab_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_163acbf2-3bdd-43ff-bff1-2ce8c190f2a0_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_5b955e99-1b02-4b30-b0da-ae976a73dd66_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Core deposit and other intangibles</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_394aa720-0b02-4d6a-a641-9e574be76de2_totalLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Carrying Value</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesAbstract_e786df0d-9fb5-47d9-80d4-66b25ae704a1_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:label id="lab_us-gaap_ReceivablesAbstract_label_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReceivablesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesAbstract" xlink:to="lab_us-gaap_ReceivablesAbstract" xlink:type="arc" order="1"/>
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    <link:label id="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember_b6ae1862-a0a9-4b0c-a615-28480dcebc52_terseLabel_en-US" xlink:label="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Voting Common Equivalent Series D</link:label>
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    <link:label id="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember_documentation_en-US" xlink:label="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Voting Common Equivalent Stock Series D</link:label>
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    <link:label id="lab_fbc_OneToFourFamilyIncludingInterestRateLocksMember_8bd2fae9-094e-442c-a003-a6d4b9bb084c_terseLabel_en-US" xlink:label="lab_fbc_OneToFourFamilyIncludingInterestRateLocksMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">One-to-four family including interest rate locks</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_bb1c3160-06c5-4792-9d9f-bbf717bb453c_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Unrealized Gain</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
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    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_d3074bca-2bf2-4a42-b3e7-8e12c1eb0122_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_PreferredStockDividendPaymentRateVariableRate_fe3cd884-70bf-4dd2-9fc3-6e36215d44d5_terseLabel_en-US" xlink:label="lab_fbc_PreferredStockDividendPaymentRateVariableRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend payment variable rate</link:label>
    <link:label id="lab_fbc_PreferredStockDividendPaymentRateVariableRate_label_en-US" xlink:label="lab_fbc_PreferredStockDividendPaymentRateVariableRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Payment Rate, Variable Rate</link:label>
    <link:label id="lab_fbc_PreferredStockDividendPaymentRateVariableRate_documentation_en-US" xlink:label="lab_fbc_PreferredStockDividendPaymentRateVariableRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Payment Rate, Variable Rate</link:label>
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    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets_6d165036-8629-456e-8703-95aa02d817ec_totalLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets acquired</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets_label_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Assets</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets_documentation_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Assets</link:label>
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    <link:label id="lab_us-gaap_OperatingCostsAndExpenses_e312b92f-a9e1-4da1-85e8-be73c9faf6b1_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingCostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total operating expense</link:label>
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    <link:label id="lab_us-gaap_FederalReserveBankStock_cc1092a0-616a-4193-a575-6598ea478e99_terseLabel_en-US" xlink:label="lab_us-gaap_FederalReserveBankStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal reserve bank stock</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, and Joint Venture Formation [Abstract]</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing_db61b56d-7166-4971-9865-6f4b647193ae_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans 90 days or greater past due and still accruing</link:label>
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    <link:label id="lab_us-gaap_OtherCommitmentsDomain_36eb4ba2-4313-41a7-b7c0-b32fc17e86cc_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Domain]</link:label>
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    <link:label id="lab_us-gaap_StockIssued1_08b2de4a-62f0-4c30-a320-558e076895e7_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued for restricted stock awards</link:label>
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    <link:label id="lab_fbc_NumberOfSecuritiesContinuousUnrealizedLossPositionMoreThanTwelveMonths_6d8eb01c-089f-4bbd-81cc-4e85a130be88_terseLabel_en-US" xlink:label="lab_fbc_NumberOfSecuritiesContinuousUnrealizedLossPositionMoreThanTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of securities continuous unrealized loss position more than twelve months</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable_c569acf0-d57c-45ea-8d2e-b03e3bf58ede_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Troubled Debt Restructuring [Table]</link:label>
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    <link:label id="lab_fbc_DirectFinancingLeaseNetInvestmentInLeasePaymentsTableTextBlock_1f4035c7-3973-4742-831d-0f8ec350785a_terseLabel_en-US" xlink:label="lab_fbc_DirectFinancingLeaseNetInvestmentInLeasePaymentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of Net Investment in Direct Financing Leases</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_fbc_DirectFinancingLeaseNetInvestmentInLeasePaymentsTableTextBlock" xlink:href="fbc-20240630.xsd#fbc_DirectFinancingLeaseNetInvestmentInLeasePaymentsTableTextBlock"/>
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    <link:label id="lab_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember_6b976314-b40f-4b29-a5fb-eeb5448e2a65_terseLabel_en-US" xlink:label="lab_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Backed Securities And Other Securities</link:label>
    <link:label id="lab_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember_6224ccf4-0134-4193-87ac-d5685bb0a4cd_verboseLabel_en-US" xlink:label="lab_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total debt securities available for sale</link:label>
    <link:label id="lab_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember_label_en-US" xlink:label="lab_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Backed Securities And Other Securities [Member]</link:label>
    <link:label id="lab_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember_documentation_en-US" xlink:label="lab_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Backed Securities And Other Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember" xlink:href="fbc-20240630.xsd#fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember" xlink:to="lab_fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_ResidentialMortgageServicingRightsMember_0426fff6-e00e-4540-9858-cb937fe9d817_verboseLabel_en-US" xlink:label="lab_fbc_ResidentialMortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights</link:label>
    <link:label id="lab_fbc_ResidentialMortgageServicingRightsMember_label_en-US" xlink:label="lab_fbc_ResidentialMortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Servicing Rights [Member]</link:label>
    <link:label id="lab_fbc_ResidentialMortgageServicingRightsMember_documentation_en-US" xlink:label="lab_fbc_ResidentialMortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative assets or liabilities which hedge the risk of overall changes in fair value of MSRs through the use of various derivatives including purchases of forward contracts on securities of Fannie Mae and Freddie Mac, the purchase/sale of U.S. Treasury futures contracts and the purchase/sale of euro dollar future contracts. These are accounted for as non-designated hedges.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ResidentialMortgageServicingRightsMember" xlink:href="fbc-20240630.xsd#fbc_ResidentialMortgageServicingRightsMember"/>
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    <link:label id="lab_fbc_WarehouseLoanCommitmentsMember_c9ce0ec4-3ee4-4665-b47c-577bd0dead49_terseLabel_en-US" xlink:label="lab_fbc_WarehouseLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warehouse loan commitments</link:label>
    <link:label id="lab_fbc_WarehouseLoanCommitmentsMember_label_en-US" xlink:label="lab_fbc_WarehouseLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warehouse Loan Commitments [Member]</link:label>
    <link:label id="lab_fbc_WarehouseLoanCommitmentsMember_documentation_en-US" xlink:label="lab_fbc_WarehouseLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warehouse Loan Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_WarehouseLoanCommitmentsMember" xlink:href="fbc-20240630.xsd#fbc_WarehouseLoanCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_WarehouseLoanCommitmentsMember" xlink:to="lab_fbc_WarehouseLoanCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue_eba3dbdf-65af-44a2-ada2-3a020fe427e3_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total collateral-dependent loans held for investment</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Owned, at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsOwnedAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentsOwnedAtFairValue"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_e0ade372-709f-4bb7-9c65-c8b91b834cfb_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities assumed</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities"/>
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    <link:label id="lab_us-gaap_ValuationTechniqueAxis_a04a5231-6272-4058-a531-5f396d1a5fbd_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ValuationTechniqueAxis"/>
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    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_5e464333-954c-4885-82ec-811a8f8a8073_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of common stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_4612680e-5704-418e-a824-ea1c07e35beb_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Decrease (increase) in other miscellaneous assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
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    <link:label id="lab_fbc_VariableInterestEntityNumberofEntities_e661e0fb-e9a8-4cfc-adcc-d666996d7ab9_terseLabel_en-US" xlink:label="lab_fbc_VariableInterestEntityNumberofEntities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of variable interest entities</link:label>
    <link:label id="lab_fbc_VariableInterestEntityNumberofEntities_label_en-US" xlink:label="lab_fbc_VariableInterestEntityNumberofEntities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Number of Entities</link:label>
    <link:label id="lab_fbc_VariableInterestEntityNumberofEntities_documentation_en-US" xlink:label="lab_fbc_VariableInterestEntityNumberofEntities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Number of Entities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_VariableInterestEntityNumberofEntities" xlink:href="fbc-20240630.xsd#fbc_VariableInterestEntityNumberofEntities"/>
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    <link:label id="lab_us-gaap_PreferredStockConvertibleConversionRatio_36ab941b-dc38-469d-831d-e2ecc7d735b0_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleConversionRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest in share conversion ratio</link:label>
    <link:label id="lab_us-gaap_PreferredStockConvertibleConversionRatio_label_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleConversionRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Convertible, Conversion Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockConvertibleConversionRatio" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockConvertibleConversionRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockConvertibleConversionRatio" xlink:to="lab_us-gaap_PreferredStockConvertibleConversionRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_MultiFamilyLoanMember_e9e33a69-3d54-41f1-9c9b-572af171b57a_terseLabel_en-US" xlink:label="lab_fbc_MultiFamilyLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family</link:label>
    <link:label id="lab_fbc_MultiFamilyLoanMember_label_en-US" xlink:label="lab_fbc_MultiFamilyLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multi-Family Loan [Member]</link:label>
    <link:label id="lab_fbc_MultiFamilyLoanMember_documentation_en-US" xlink:label="lab_fbc_MultiFamilyLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Multi-Family Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_MultiFamilyLoanMember" xlink:href="fbc-20240630.xsd#fbc_MultiFamilyLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_MultiFamilyLoanMember" xlink:to="lab_fbc_MultiFamilyLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_2e657f2d-29cf-4dba-8ac9-2fc94093b290_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_MeasureAxis"/>
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    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare_1f2b2774-1a3f-4d72-a1a1-a9a826757522_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation Preference Per Share (in USD per share)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityLiquidationPreferencePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:to="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_2a630023-710a-470a-816a-a20423c7ce27_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_ImpairedLoansFairValueDisclosure_06d37f79-117d-4d4f-b5ab-48b0a53dcf5c_terseLabel_en-US" xlink:label="lab_fbc_ImpairedLoansFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Certain impaired loans</link:label>
    <link:label id="lab_fbc_ImpairedLoansFairValueDisclosure_label_en-US" xlink:label="lab_fbc_ImpairedLoansFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impaired Loans, Fair Value Disclosure</link:label>
    <link:label id="lab_fbc_ImpairedLoansFairValueDisclosure_documentation_en-US" xlink:label="lab_fbc_ImpairedLoansFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impaired Loans, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ImpairedLoansFairValueDisclosure" xlink:href="fbc-20240630.xsd#fbc_ImpairedLoansFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_afc3f909-53c6-4aab-b268-68614411f03e_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance and exercise of stock (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
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    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_a5de2b06-926d-4214-aabd-8629bc64a68f_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities at fair value</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable_label_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Option, Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueOptionQuantitativeDisclosuresTable"/>
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    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_6cba50b3-68e3-4522-91b8-9b6647416b44_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in usd per share)</link:label>
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    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_28a02245-f6f9-4a68-a543-33b876fecd19_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Sold under Agreements to Repurchase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchase"/>
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    <link:label id="lab_us-gaap_DirectFinancingLeaseNetInvestmentInLeaseAfterAllowanceForCreditLoss_b11e7228-c690-4382-9c01-41438261cddf_terseLabel_en-US" xlink:label="lab_us-gaap_DirectFinancingLeaseNetInvestmentInLeaseAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying value of net investment in leases</link:label>
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    <link:label id="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_e676292d-b566-41bd-b8c2-9904a9043d45_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net interest income after provision for credit loan losses</link:label>
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    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_e26f67b3-efe2-481e-9cf9-2c26f0e0a0d1_totalLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest income</link:label>
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    <link:label id="lab_fbc_CommercialAndIndustrialLoanAndLeaseFinancingMember_7591753f-6bec-4773-9f5c-3dc07ac966e3_terseLabel_en-US" xlink:label="lab_fbc_CommercialAndIndustrialLoanAndLeaseFinancingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial and industrial loans and lease financing</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareBasicLineItems_e3442bd1-1533-4ca9-b985-e2b24c436a8a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
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    <link:label id="lab_fbc_LoanHeldForInvestmentFairValueDisclosure_895601b9-64be-4a62-93be-2d8031e9c0e7_terseLabel_en-US" xlink:label="lab_fbc_LoanHeldForInvestmentFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held-for-investment</link:label>
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    <link:label id="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetLineItems_4c049f84-963e-4740-8c34-04193d36d919_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation, Less than Wholly Owned Subsidiary, Parent Ownership Interest, Effects of Changes, Net [Line Items]</link:label>
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    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_1e141de3-7b79-4e47-927c-0e85fe6bdc26_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Assets:</link:label>
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    <link:label id="lab_us-gaap_MarketableSecurities_label_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities</link:label>
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    <link:label id="lab_us-gaap_OtherCommitmentsAxis_7b12814b-d4da-4402-b193-b356ab380d24_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Axis]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsAxis_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Axis]</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_b4ff2860-b839-40f5-8ee6-c0faa619501e_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_95b62535-1b1b-4797-abeb-1316ed8c66a5_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from five to ten years</link:label>
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    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_8f9feb76-2a69-47a7-82e7-a0a52d35feae_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other intangible assets</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_719defb9-847d-4acd-acbf-2fb27bed121f_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
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    <link:label id="lab_fbc_FinancingReceivableAdditionalSale_ff883a79-7ed9-4286-83b6-6ad06bd1ec90_terseLabel_en-US" xlink:label="lab_fbc_FinancingReceivableAdditionalSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing receivable, additional sale</link:label>
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    <link:label id="lab_fbc_LoansHeldForSaleMember_b222dc4b-1c31-4158-8b1a-8ae6b6be24b0_terseLabel_en-US" xlink:label="lab_fbc_LoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for sale</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_1cfb4f93-6158-46a6-b5b2-96f455b65d12_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average discount rate %</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt_73dd0b34-712c-4c97-88c4-5dfbb5ef3acb_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in short-term borrowed funds</link:label>
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    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableDeferredOriginationCosts_47728c15-2015-4a5f-a59e-1639e7c6d302_terseLabel_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableDeferredOriginationCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plus: deferred origination costs</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_b0385b86-91c4-4250-abd1-b396e3ad1565_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) financing activities</link:label>
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    <link:label id="lab_us-gaap_BankOwnedLifeInsuranceIncome_e6d33263-0d64-4db7-80e7-cccf99a9ba2e_terseLabel_en-US" xlink:label="lab_us-gaap_BankOwnedLifeInsuranceIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bank-owned life insurance</link:label>
    <link:label id="lab_us-gaap_BankOwnedLifeInsuranceIncome_label_en-US" xlink:label="lab_us-gaap_BankOwnedLifeInsuranceIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bank Owned Life Insurance Income</link:label>
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    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeLoss_33c9e690-521b-4e4f-b737-d4cf3f6eeb10_verboseLabel_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtFairValue_d23b12bd-fda2-479a-b6df-aa08dc391945_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowed funds</link:label>
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    <link:label id="lab_dei_EntityRegistrantName_1cccdf81-7847-4465-adb3-f5676c7f62e1_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
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    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis_4f52361c-a7fc-4ddd-aeb0-ced2f2df3d86_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Axis]</link:label>
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    <link:label id="lab_us-gaap_IntangibleAssetsDisclosureTextBlock_80762a1a-fae1-41e9-919e-04de0bb8102a_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets</link:label>
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    <link:label id="lab_us-gaap_EquitySecuritiesFVNIAbstract_2744d5ac-e637-42b9-b705-f5d7bac2af32_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFVNIAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities:</link:label>
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    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
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    <link:label id="lab_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecuritiesCurrent_9ce857b7-8566-47c4-aed6-f66fb8c8f0a5_terseLabel_en-US" xlink:label="lab_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecuritiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInDeposits_611b0e4d-96f6-4431-8161-3ff486c74731_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net decrease in deposits</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDeposits" xlink:to="lab_us-gaap_IncreaseDecreaseInDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquityAndEquityParValueAbstract_c635f697-eb58-4de1-9f5e-ab2dcad75ac2_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityParValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Par Value</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentBeforeReclassificationAdjustmentsNetOfTax_58f119a2-9a0e-4d61-869b-aff8a058f042_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentBeforeReclassificationAdjustmentsNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in pension and post-retirement obligations, net of tax of $0; $(1); $(1) and $(1)</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_6eeb48b1-7891-4f53-b726-db9bf15e3315_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Other Observable Inputs (Level 2)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_MarketableSecuritiesGrossUnrealizedGain_d26ab59c-4d9f-4b1c-8040-50bb78dbf6dd_terseLabel_en-US" xlink:label="lab_fbc_MarketableSecuritiesGrossUnrealizedGain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Unrealized Gain</link:label>
    <link:label id="lab_fbc_MarketableSecuritiesGrossUnrealizedGain_label_en-US" xlink:label="lab_fbc_MarketableSecuritiesGrossUnrealizedGain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities Gross Unrealized Gain</link:label>
    <link:label id="lab_fbc_MarketableSecuritiesGrossUnrealizedGain_documentation_en-US" xlink:label="lab_fbc_MarketableSecuritiesGrossUnrealizedGain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marketable Securities Gross Unrealized Gain</link:label>
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    <link:label id="lab_us-gaap_OffsettingAssetsTable_876821cd-e188-4ad5-8f8e-b18a75350be9_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table]</link:label>
    <link:label id="lab_us-gaap_OffsettingAssetsTable_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OffsettingAssetsTable"/>
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    <link:label id="lab_fbc_FairValueOptionLoansHeldAsAssets_b093520a-e80e-47ae-9e37-3aca124b72f9_verboseLabel_en-US" xlink:label="lab_fbc_FairValueOptionLoansHeldAsAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_fbc_FairValueOptionLoansHeldAsAssets_label_en-US" xlink:label="lab_fbc_FairValueOptionLoansHeldAsAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Loans Held as Assets</link:label>
    <link:label id="lab_fbc_FairValueOptionLoansHeldAsAssets_documentation_en-US" xlink:label="lab_fbc_FairValueOptionLoansHeldAsAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Loans Held as Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FairValueOptionLoansHeldAsAssets" xlink:href="fbc-20240630.xsd#fbc_FairValueOptionLoansHeldAsAssets"/>
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    <link:label id="lab_srt_SegmentGeographicalDomain_91502bbf-debf-4165-8f31-bdb12771b65d_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment, Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_56682c06-a93f-43ed-bd8c-3fc86b88978e_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance and exercise of stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_35a1c4f7-98c7-440c-bfba-cd660dc7542b_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_RestatementDateAxis"/>
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    <link:label id="lab_dei_Security12bTitle_38935843-7f77-482a-a9b3-e70308be1e23_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_04e8e9cc-bdc6-47e7-b489-29968b7e134a_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock at par 0.01 (666,666,666 and 300,000,000 shares authorized; 358,864,464 and 248,051,930&#8233; shares issued; and 351,304,364 and 240,688,790 shares outstanding, respectively)</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_46bd3ade-66ad-4010-8567-8c7f74959d29_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_1808cf56-a404-49f6-bf79-46f8e104c45e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Past Due Loans</link:label>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialAssetPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetPastDueMember" xlink:to="lab_us-gaap_FinancialAssetPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_de7a6250-a18c-4aab-b958-1bf2922bca46_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Payment Arrangement [Abstract]</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
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    <link:label id="lab_us-gaap_FairValueOptionLoansHeldAsAssetsAggregateDifference_b8c0e87a-eb1c-44e7-8a8e-fea9db7ce602_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionLoansHeldAsAssetsAggregateDifference" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Over / (Under) UPB</link:label>
    <link:label id="lab_us-gaap_FairValueOptionLoansHeldAsAssetsAggregateDifference_label_en-US" xlink:label="lab_us-gaap_FairValueOptionLoansHeldAsAssetsAggregateDifference" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Loans Held as Assets, Aggregate Difference</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionLoansHeldAsAssetsAggregateDifference" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueOptionLoansHeldAsAssetsAggregateDifference"/>
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    <link:label id="lab_fbc_SwapFHLBMember_cc6ae1e2-05cb-4ced-afa1-21049b2f66ed_terseLabel_en-US" xlink:label="lab_fbc_SwapFHLBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Swap FHLB</link:label>
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    <link:label id="lab_fbc_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_a3a553b5-566f-4add-ad30-e2f1d0925f86_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mezzanine preferred stock (in shares)</link:label>
    <link:label id="lab_fbc_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_fbc_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Shares, New Issues</link:label>
    <link:label id="lab_fbc_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_documentation_en-US" xlink:label="lab_fbc_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Shares, New Issues</link:label>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateOfAmountsDueAbstract_017c3778-001f-482c-95be-125c2e4db82d_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateOfAmountsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Interest Rate</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateOfAmountsDueAbstract_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateOfAmountsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Average Interest Rate [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateOfAmountsDueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryAverageInterestRateOfAmountsDueAbstract"/>
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    <link:label id="lab_us-gaap_ContractualInterestRateReductionMember_80ae54d6-b431-4bcc-a5f6-0cbe06a7d84d_terseLabel_en-US" xlink:label="lab_us-gaap_ContractualInterestRateReductionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Reduction</link:label>
    <link:label id="lab_us-gaap_ContractualInterestRateReductionMember_label_en-US" xlink:label="lab_us-gaap_ContractualInterestRateReductionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Interest Rate Reduction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualInterestRateReductionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ContractualInterestRateReductionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractualInterestRateReductionMember" xlink:to="lab_us-gaap_ContractualInterestRateReductionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_f70305db-71fb-42fe-82d8-4dfa045e7ff8_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember_bfcd1b59-0299-4400-8f90-2a6811f80376_terseLabel_en-US" xlink:label="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net return on mortgage servicing rights</link:label>
    <link:label id="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember_label_en-US" xlink:label="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights (MSR) Impairment (Recovery) [Member]</link:label>
    <link:label id="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember_documentation_en-US" xlink:label="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the net return on mortgage servicing asset.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember" xlink:href="fbc-20240630.xsd#fbc_MortgageServicingRightsMSRImpairmentRecoveryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember" xlink:to="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_07621df5-2b00-4110-9b77-7a285d52f8a6_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CASH FLOWS FROM FINANCING ACTIVITIES:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_7cb2fbbb-b962-4683-9845-ae101ff7a953_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock - Series A (See Note 17 - Mezzanine and Stockholders Equity)</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_faccea84-bf31-4017-b1e1-b16a51834ece_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SubordinatedNotesMaturingIn2030Member_41b27f11-3999-4531-9d7c-ab8bda91a61b_terseLabel_en-US" xlink:label="lab_fbc_SubordinatedNotesMaturingIn2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated notes maturing in 2030</link:label>
    <link:label id="lab_fbc_SubordinatedNotesMaturingIn2030Member_label_en-US" xlink:label="lab_fbc_SubordinatedNotesMaturingIn2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Notes Maturing In 2030 [Member]</link:label>
    <link:label id="lab_fbc_SubordinatedNotesMaturingIn2030Member_documentation_en-US" xlink:label="lab_fbc_SubordinatedNotesMaturingIn2030Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subordinated Notes Maturing In 2030</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SubordinatedNotesMaturingIn2030Member" xlink:href="fbc-20240630.xsd#fbc_SubordinatedNotesMaturingIn2030Member"/>
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    <link:label id="lab_us-gaap_ValuationTechniqueDomain_4f7a78f9-88e6-4128-a8bb-1dbe7c436597_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_9450f46f-f3a0-412a-8876-d7417b0e1c4c_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic (loss) earnings per common share (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_f88e87f2-241d-4b41-be9f-a9485f53f19a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (loss) earnings per common share (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_08138eaa-636f-4b80-aee6-ef47c3e6e5bc_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from common stock and warrants issued</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_01add2ab-f1b6-4bc3-b2ec-b41340fe845e_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating cash flows from operating leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable_fadd2f25-0c32-4777-a471-97cc3833eecd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Impaired Financing Receivable [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Impaired Financing Receivable [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfImpairedFinancingReceivableTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:to="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_0825ea66-5ecf-4fb9-884b-4e837eabcc75_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock - Series B (See Note 17 - Mezzanine and Stockholders Equity )</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_3e41f983-0926-45fe-998e-4af1db956964_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_8a558a6b-d9fd-4f36-a4a9-582f78efa74a_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Carrying Amount, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_190b5da1-c8fd-4218-84d5-adfd56f2c69d_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized stock-based compensation cost for options</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioPreviouslyReportedMember_3ec597a0-7bd7-480d-ba40-97572cedf4e4_terseLabel_en-US" xlink:label="lab_srt_ScenarioPreviouslyReportedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Previously Reported</link:label>
    <link:label id="lab_srt_ScenarioPreviouslyReportedMember_label_en-US" xlink:label="lab_srt_ScenarioPreviouslyReportedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Previously Reported [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioPreviouslyReportedMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ScenarioPreviouslyReportedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioPreviouslyReportedMember" xlink:to="lab_srt_ScenarioPreviouslyReportedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtAndEquitySecuritiesGainLoss_70f5dfd1-2922-411a-a7f1-0a934ecbbc8c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtAndEquitySecuritiesGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net (loss) on securities</link:label>
    <link:label id="lab_us-gaap_DebtAndEquitySecuritiesGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtAndEquitySecuritiesGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt and Equity Securities, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtAndEquitySecuritiesGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtAndEquitySecuritiesGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtAndEquitySecuritiesGainLoss" xlink:to="lab_us-gaap_DebtAndEquitySecuritiesGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_15e8ef6b-6172-4505-a32f-96c7c7182707_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebt_a8266fb2-cb3b-4bf2-a7de-6f275750b5dd_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from long-term borrowed funds</link:label>
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    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_755f1866-bbb9-4949-9f17-30b885331a8c_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee Arrangements</link:label>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Leases [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeLeasesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths_082b7a4d-3008-4664-b78f-bf7dcaa6fa1c_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Year One</link:label>
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    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableUndiscountedExcessAmount_cd5f4044-3bbc-4cd3-a8e7-5c0812ee7887_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unearned income</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableUndiscountedExcessAmount_a471781a-8bfa-4e4e-b08e-60ae47a97626_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: unearned income</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableUndiscountedExcessAmount"/>
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    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_afe16e62-4ccd-4f0f-85a6-1764889a18b8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Payment Arrangement, Option, Activity</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock"/>
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    <link:label id="lab_fbc_GainLossOnSalesOfMortgageServicingRights_16e15f61-ad01-4624-a970-28ee285165de_terseLabel_en-US" xlink:label="lab_fbc_GainLossOnSalesOfMortgageServicingRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net return on mortgage servicing rights</link:label>
    <link:label id="lab_fbc_GainLossOnSalesOfMortgageServicingRights_label_en-US" xlink:label="lab_fbc_GainLossOnSalesOfMortgageServicingRights" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain Loss on Sales of Mortgage Servicing Rights</link:label>
    <link:label id="lab_fbc_GainLossOnSalesOfMortgageServicingRights_documentation_en-US" xlink:label="lab_fbc_GainLossOnSalesOfMortgageServicingRights" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net gain (loss) resulting from the sales of mortgage servicing rights.</link:label>
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    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldForSale_dd8f4412-ed87-4ed5-ad0c-529b53383948_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest , loans and leases held-for-sale</link:label>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldForSale_label_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Fee Income, Loan and Lease, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldForSale" xlink:to="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_1063bce7-1b0d-44db-9b43-b938c96a36ce_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Allowance for credit losses on loans and leases</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_119cec7f-b933-4d0f-a54b-0164a8fdc0e0_negatedLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses on loans and leases</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_6a23d275-1a76-43bd-a8cf-08bf399af8f5_periodStartLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, beginning of period</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_d2fb32dc-2ed4-41ae-bada-072a0ea24d8d_periodEndLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance, end of period</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_54e05bcd-f32e-49ad-9c6e-bbc5d69272f3_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses on loans and leases</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest"/>
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    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_f639594c-12c9-439e-afc5-70999e64956f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts Netted in the Statements of Condition</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Liability Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeAssetFairValueGrossLiability"/>
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    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_1d369efa-7034-45c8-93fb-7a83275464bf_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation expense</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
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    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_31daa15f-7565-465a-991b-14eef064b22e_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
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    <link:label id="lab_fbc_ScheduleOfTradingAndAvailableForSaleSecuritiesTableTextBlock_eb5f1f9d-9c14-423f-8c0f-eb0f55310a3c_terseLabel_en-US" xlink:label="lab_fbc_ScheduleOfTradingAndAvailableForSaleSecuritiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Held-to-Maturity and Available-for-Sale Securities</link:label>
    <link:label id="lab_fbc_ScheduleOfTradingAndAvailableForSaleSecuritiesTableTextBlock_label_en-US" xlink:label="lab_fbc_ScheduleOfTradingAndAvailableForSaleSecuritiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Trading and Available-for-sale Securities [Table Text Block]</link:label>
    <link:label id="lab_fbc_ScheduleOfTradingAndAvailableForSaleSecuritiesTableTextBlock_documentation_en-US" xlink:label="lab_fbc_ScheduleOfTradingAndAvailableForSaleSecuritiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The table text block of the schedule of trading and available-for-sale securities.</link:label>
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    <link:label id="lab_us-gaap_SensitivityAnalysisOfFairValueOfInterestsContinuedToBeHeldByTransferorServicingAssetsOrLiabilitiesImpactOf20PercentAdverseChangeInPrepaymentSpeed_2b728f2c-c7b3-4c10-80c6-8cb4b28574eb_terseLabel_en-US" xlink:label="lab_us-gaap_SensitivityAnalysisOfFairValueOfInterestsContinuedToBeHeldByTransferorServicingAssetsOrLiabilitiesImpactOf20PercentAdverseChangeInPrepaymentSpeed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Constant prepayment rate</link:label>
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    <link:label id="lab_us-gaap_OtherCommitmentsTable_d304a908-adee-4ef7-9855-3ee78a3b361f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Table]</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_edaebdad-5a84-4463-ad41-774390df98ad_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024</link:label>
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    <link:label id="lab_dei_DocumentPeriodEndDate_13024431-3e26-4f87-8203-d6e46521357d_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentPeriodEndDate"/>
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    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_5184b061-230d-4786-bb83-1f4d9620ed09_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityOwnershipPercentage_f2256ab7-142d-47f8-bb16-72c3a85c2fa1_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">VIE ownership percentage</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Qualitative or Quantitative Information, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityOwnershipPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VariableInterestEntityOwnershipPercentage"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_062c4e8f-1d49-47c5-a714-498d5e5715d2_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_a9eab598-9f7c-4d5f-877c-62dae503810f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-vested balance (in shares)</link:label>
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    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
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    <link:label id="lab_us-gaap_SpecialMentionMember_184edd84-679c-48b2-9211-d1efd3d6b085_terseLabel_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Special Mention</link:label>
    <link:label id="lab_us-gaap_SpecialMentionMember_label_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Special Mention [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SpecialMentionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SpecialMentionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SpecialMentionMember" xlink:to="lab_us-gaap_SpecialMentionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_28b52c85-4f2a-4dad-85ad-ea6030da0764_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
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    <link:label id="lab_dei_DocumentTransitionReport_33dbf0ca-0d8c-408e-a8d4-f5deffc47c36_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentTransitionReport"/>
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    <link:label id="lab_us-gaap_SensitivityAnalysisOfFairValueOfInterestsContinuedToBeHeldByTransferorServicingAssetsOrLiabilitiesImpactOf10PercentAdverseChangeInPrepaymentSpeed_babb0251-4199-47d5-b888-e0d81e60e274_terseLabel_en-US" xlink:label="lab_us-gaap_SensitivityAnalysisOfFairValueOfInterestsContinuedToBeHeldByTransferorServicingAssetsOrLiabilitiesImpactOf10PercentAdverseChangeInPrepaymentSpeed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Constant prepayment rate</link:label>
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    <link:label id="lab_us-gaap_ServicingAssetsAtFairValueTable_93c741a7-51a9-486e-bf60-e4b93af3f31d_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetsAtFairValueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Servicing Assets at Fair Value [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetsAtFairValueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ServicingAssetsAtFairValueTable"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract_36a94dd1-e126-4f5d-ae58-e0a8bbcb45db_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost Basis by Closing Year</link:label>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_b7d45a33-cac6-405f-a794-e6b9a33de4c8_verboseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">(Accumulated deficit)/Retained Earnings</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetainedEarningsMember"/>
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    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
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    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralLineItems_b06bf080-bf6e-4835-82ed-30824a4f8b4d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments Owned and Pledged as Collateral [Line Items]</link:label>
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