Business Segment Information - Reconciliation of Segment Depreciation and Amortization Expense to Consolidated Depreciation and Amortization Expense (Details) - USD ($) $ in Thousands	12 Months Ended
	Jun. 30, 2019	Jun. 24, 2018	Jun. 25, 2017
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	$ 23,003	$ 22,585	$ 20,368
Operating Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	19,917	19,994	17,803
Operating Segments [Member] | Polyester [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	16,068	15,893	13,921
Operating Segments [Member] | Nylon [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	2,083	2,197	2,125
Operating Segments [Member] | Brazil [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	1,537	1,648	1,119
Operating Segments [Member] | Other Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	229	256	638
Other Depreciation and Amortization Expense [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	$ 3,086	$ 2,591	$ 2,565