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Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Jun. 28, 2020	Jun. 30, 2019	Jun. 24, 2018
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 474,162	$ 592,151	$ 601,807
Other current assets	11,763	16,356
Property, plant and equipment, net	204,246	206,787
Other operating lease assets	1,503
Other non-current assets	548	671
Investments in unconsolidated affiliates	2,171	114,320
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	396,935	447,372
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	263,496	287,608
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	42,020	57,055
Operating Segments [Member] | Brazil [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	49,967	67,490
Operating Segments [Member] | Asia [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	41,452	35,219
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	48,600	10,327
Property, plant and equipment, net	23,676	18,664
Other non-current assets	1,277	1,468
Investments in unconsolidated affiliates	$ 2,171	$ 114,320

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