Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Mar. 29, 2020	Jun. 30, 2019
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 543,042	$ 592,151
Other current assets	18,477	16,356
Other non-current assets	2,187	2,841
Investments in unconsolidated affiliates	58,854	114,320
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	445,667	447,372
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	295,192	287,608
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	50,905	57,055
Operating Segments [Member] | Brazil [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	54,040	67,490
Operating Segments [Member] | Asia [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	45,530	35,219
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	7,235	10,327
Other PP&E	24,412	18,664
Other non-current operating lease assets	1,599
Other non-current assets	5,275	1,468
Investments in unconsolidated affiliates	$ 58,854	$ 114,320