Business Segment Information - Reconciliation of Segment Depreciation and Amortization Expense to Consolidated Depreciation and Amortization Expense (Details) - USD ($) $ in Thousands	12 Months Ended
	Jun. 24, 2018	Jun. 25, 2017	Jun. 26, 2016
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	$ 22,585	$ 20,368	$ 17,528
Operating Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	19,994	17,803	14,792
Operating Segments [Member] | Polyester [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	15,893	13,921	11,188
Operating Segments [Member] | Nylon [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	2,197	2,125	1,899
Operating Segments [Member] | International [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	1,648	1,119	885
Operating Segments [Member] | Other Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	256	638	820
Other Depreciation and Amortization Expense [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Depreciation and amortization expense	$ 2,591	$ 2,565	$ 2,736