Investment Securities - Summary of Investment Securities (Details) - USD ($) $ in Millions	Sep. 30, 2024	Dec. 31, 2023
Debt securities available-for-sale
Amortized Cost	$ 10,511
Equity securities:
Fair Value	14	$ 14
Total Securities
Amortized Cost	11,172	9,958
Gross Unrealized Gain	87	62
Gross Unrealized Loss	734	861
Fair Value	10,525	9,159
Amortized cost of investment securities	3
Interest receivable	$ 35	$ 38
Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]	Other assets	Other assets
Mortgage Backed Securities And Other Securities
Debt securities available-for-sale
Amortized Cost	$ 11,156	$ 9,942
Gross Unrealized Gain	87	62
Gross Unrealized Loss	732	859
Fair Value	10,511	9,145
Mortgage-Related Debt Securities:
Debt securities available-for-sale
Amortized Cost	8,908	7,035
Gross Unrealized Gain	81	56
Gross Unrealized Loss	464	528
Fair Value	8,525	6,563
GSE certificates
Debt securities available-for-sale
Amortized Cost	1,296	1,366
Gross Unrealized Gain	2	1
Gross Unrealized Loss	123	146
Fair Value	1,175	1,221
GSE collateralized mortgage obligations
Debt securities available-for-sale
Amortized Cost	7,452	5,495
Gross Unrealized Gain	67	48
Gross Unrealized Loss	341	381
Fair Value	7,178	5,162
Private label collateralized mortgage obligations
Debt securities available-for-sale
Amortized Cost	160	174
Gross Unrealized Gain	12	7
Gross Unrealized Loss	0	1
Fair Value	172	180
Other Debt Securities:
Debt securities available-for-sale
Amortized Cost	2,248	2,907
Gross Unrealized Gain	6	6
Gross Unrealized Loss	268	331
Fair Value	1,986	2,582
U. S. Treasury obligations
Debt securities available-for-sale
Amortized Cost		198
Gross Unrealized Gain		0
Gross Unrealized Loss		0
Fair Value		198
GSE debentures
Debt securities available-for-sale
Amortized Cost	1,502	1,899
Gross Unrealized Gain	0	1
Gross Unrealized Loss	248	291
Fair Value	1,254	1,609
Asset-backed securities
Debt securities available-for-sale
Amortized Cost	246	307
Gross Unrealized Gain	0	0
Gross Unrealized Loss	3	5
Fair Value	243	302
Municipal bonds
Debt securities available-for-sale
Amortized Cost	6	6
Gross Unrealized Gain	0	0
Gross Unrealized Loss	0	0
Fair Value	6	6
Corporate bonds
Debt securities available-for-sale
Amortized Cost	364	365
Gross Unrealized Gain	0	0
Gross Unrealized Loss	7	22
Fair Value	357	343
Foreign notes
Debt securities available-for-sale
Amortized Cost	35	35
Gross Unrealized Gain	0	0
Gross Unrealized Loss	0	1
Fair Value	35	34
Capital trust notes
Debt securities available-for-sale
Amortized Cost	95	97
Gross Unrealized Gain	6	5
Gross Unrealized Loss	10	12
Fair Value	91	90
Equity securities:
Equity securities:
Amortized Cost	16	16
Gross Unrealized Loss	2	2
Fair Value	14	14
Mutual funds
Equity securities:
Amortized Cost	16	16
Gross Unrealized Loss	2	2
Fair Value	$ 14	$ 14

Debt Securities, Available For Sale, Excluding Interest and Equity Securities

No definition available.

Name:	fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecurities
Namespace Prefix:	fbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Debt Securities, Available For Sale, Excluding Interest and Equity Securities, Current

+ References

No definition available.

+ Details

Name:	fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecuritiesCurrent
Namespace Prefix:	fbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Equity Securities, Unrealized Loss

+ References

No definition available.

+ Details

Name:	fbc_EquitySecuritiesUnrealizedLoss
Namespace Prefix:	fbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Investment Securities, Available-for-Sale, Amortized Cost, Excluding Accrued Interest, after Allowance for Credit Loss

+ References

No definition available.

+ Details

Name:	fbc_InvestmentSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss
Namespace Prefix:	fbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Marketable Securities Gross Unrealized Gain

+ References

No definition available.

+ Details

Name:	fbc_MarketableSecuritiesGrossUnrealizedGain
Namespace Prefix:	fbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Marketable Securities Gross Unrealized Loss

+ References

No definition available.

+ Details

Name:	fbc_MarketableSecuritiesGrossUnrealizedLoss
Namespace Prefix:	fbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount, before tax, of unrealized gain in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 320
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481800/320-10-50-2

+ Details

Name:	us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, before tax, of unrealized loss in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 320
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481800/320-10-50-2

+ Details

Name:	us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_AvailableForSaleSecuritiesAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount, after allowance for credit loss, of accrued interest on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 320
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481800/320-10-50-2A

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479130/326-30-45-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 3A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479106/326-30-50-3A

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 3B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479106/326-30-50-3B

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Indicates line item in statement of financial position that includes accrued interest, after allowance for credit loss, on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 3A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479106/326-30-50-3A

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList
Namespace Prefix:	us-gaap_
Data Type:	enum2:enumerationSetItemType
Balance Type:	na
Period Type:	instant

- Definition

Amortized cost excluding accrued interest, after allowance for credit loss, of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 326
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479130/326-30-45-1

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount excluding accrued interest, of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_EquitySecuritiesFVNIAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI), classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(2))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483467/210-10-45-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482736/825-10-45-1A

+ Details

Name:	us-gaap_EquitySecuritiesFvNi
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Cost of investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI). Excludes equity method investment and investment in equity security without readily determinable fair value.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

+ Details

Name:	us-gaap_EquitySecuritiesFvNiCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_MarketableSecuritiesAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_FinancialInstrumentAxis=fbc_MortgageBackedSecuritiesAndOtherSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_MortgageBackedSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_CollateralizedMortgageObligationsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_DebtSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_USTreasurySecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_AssetBackedSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_MunicipalBondsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_CorporateBondSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=fbc_ForeignNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_CorporateNoteSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_EquitySecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_MutualFundMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: