Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Jun. 30, 2019	Jun. 24, 2018	Jun. 25, 2017
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 592,151	$ 601,807	$ 571,503
Other current assets	16,356	6,529
Property, plant and equipment, net	206,787	205,516
Other non-current assets	671	3,080
Investments in unconsolidated affiliates	114,320	112,639
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	447,372	436,645
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	287,608	284,261
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	57,055	57,378
Operating Segments [Member] | Brazil [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	67,490	59,657
Operating Segments [Member] | Asia [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	35,219	35,349
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	10,327	30,945
Property, plant and equipment, net	18,664	17,373
Other non-current assets	1,468	4,205
Investments in unconsolidated affiliates	$ 114,320	$ 112,639