Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Jun. 27, 2021	Jun. 28, 2020	Jun. 30, 2019
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 555,368	$ 474,162	$ 592,151
Other current assets	12,364	11,763
Property, plant and equipment, net	201,696	204,246
Other operating lease assets	1,116	1,503
Other non-current assets	14,625	4,131
Investments in unconsolidated affiliates	2,159	2,171
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	481,044	396,935
Operating Segments [Member] | Polyester
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	285,939	263,496
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	68,034	42,020
Operating Segments [Member] | Brazil [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	85,950	49,967
Operating Segments [Member] | Asia [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	41,121	41,452
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	48,972	48,600
Property, plant and equipment, net	21,175	23,676
Other non-current assets	902	1,277
Investments in unconsolidated affiliates	$ 2,159	$ 2,171