Business Segment Information - Reconciliation of Segment Depreciation and Amortization Expense to Consolidated Depreciation and Amortization Expense (Details) - USD ($) $ in Thousands	12 Months Ended
	Jun. 27, 2021	Jun. 28, 2020	Jun. 30, 2019
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	$ 25,528	$ 23,653	$ 23,003
Operating Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	22,369	20,659	19,917
Operating Segments [Member] | Polyester
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	18,637	16,904	16,068
Operating Segments [Member] | Nylon [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	1,769	1,917	2,083
Operating Segments [Member] | Brazil [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	1,315	1,385	1,537
Operating Segments [Member] | Other Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	648	453	229
Other Depreciation and Amortization Expense [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	$ 3,159	$ 2,994	$ 3,086