Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Mar. 31, 2019	Jun. 24, 2018
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 608,791	$ 601,807
Other current assets	16,365	6,529
Property, plant and equipment, net	207,303	205,516
Other non-current assets	3,598	6,070
Investments in unconsolidated affiliates	114,747	112,639
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	452,940	436,645
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	291,625	284,261
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	60,904	57,378
Operating Segments [Member] | International [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	100,411	95,006
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	19,496	30,945
Property, plant and equipment, net	19,091	17,373
Other non-current assets	2,516	4,205
Investments in unconsolidated affiliates	$ 114,748	$ 112,639