Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Jun. 24, 2018	Jun. 25, 2017	Jun. 26, 2016
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 601,807	$ 571,503	$ 525,442
Other current assets	6,529	6,468
Property, plant and equipment, net	205,516	203,388
Other non-current assets	3,080	613
Investments in unconsolidated affiliates	112,639	119,513
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	436,645	409,432	373,232
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	284,261	270,819	243,093
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	57,378	57,789	63,141
Operating Segments [Member] | International [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	95,006	80,824	66,998
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	30,945	27,375	13,337
Property, plant and equipment, net	17,373	14,904	16,597
Other non-current assets	4,205	279	4,864
Investments in unconsolidated affiliates	$ 112,639	$ 119,513	$ 117,412