Business Segment Information - Reconciliation of Segment Depreciation and Amortization Expense to Consolidated Depreciation and Amortization Expense (Details) - USD ($) $ in Thousands	12 Months Ended
	Jun. 28, 2020	Jun. 28, 2020	Jun. 30, 2019	Jun. 24, 2018
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	$ 23,653	$ 23,653	$ 23,003	$ 22,585
Operating Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense		20,659	19,917	19,994
Operating Segments [Member] | Polyester [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense		16,904	16,068	15,893
Operating Segments [Member] | Nylon [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense		1,917	2,083	2,197
Operating Segments [Member] | Brazil [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense		1,385	1,537	1,648
Operating Segments [Member] | Other Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense		453	229	256
Other Depreciation and Amortization Expense [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense		$ 2,994	$ 3,086	$ 2,591