Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Sep. 30, 2018	Jun. 24, 2018
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 608,118	$ 601,807
Other current assets	15,658	6,529
Property, plant and equipment, net	203,820	205,516
Other non-current assets	5,988	6,070
Investments in unconsolidated affiliates	112,726	112,639
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	436,901	436,645
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	288,871	284,261
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	59,284	57,378
Operating Segments [Member] | International [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	88,746	95,006
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	36,713	30,945
Property, plant and equipment, net	17,261	17,373
Other non-current assets	4,517	4,205
Investments in unconsolidated affiliates	$ 112,726	$ 112,639