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Employee Retirement Plans - Defined Contribution Plans - Narrative (Details) $ in Millions | 12 Months Ended
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Dec. 30, 2023 USD ($) defined_contribution_plan | Dec. 31, 2022 USD ($) | Jan. 02, 2021 USD ($)
Defined Benefit Plan Disclosure [Line Items] |  |  |
Number of defined contribution plans | defined_contribution_plan | 2 |  |
Hourly Savings Plan |  |  |
Defined Benefit Plan Disclosure [Line Items] |  |  |
Defined contribution plan, cost recognized | $ 0.9 | $ 0.8 |
Salaried Savings Plan |  |  |
Defined Benefit Plan Disclosure [Line Items] |  |  |
Defined contribution plan, cost recognized | 2.5 | $ 4.0 |
Defined contribution plan, prior year cost | $ 0.0 |  | $ 2.1

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- Definition Defined Contribution Plan, Cost, Prior Year + References No definition available. + Details
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Namespace Prefix: | bxc_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition Defined Contribution Plan, Number of Plans + References No definition available. + Details
Name: | bxc_DefinedContributionPlanNumberofPlans
Namespace Prefix: | bxc_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | duration

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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
Name: | us-gaap_DefinedBenefitPlanDisclosureLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Amount of cost for defined contribution plan. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 715 -SubTopic 70 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Publisher FASB -URI https://asc.fasb.org//1943274/2147480794/715-70-50-1 + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Details
Name: | us-gaap_RetirementPlanNameAxis=bxc_HourlySavingsPlanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_RetirementPlanNameAxis=bxc_SalariedSavingsPlanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |