Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Mar. 28, 2021	Jun. 28, 2020
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 528,372	$ 474,162
Other current assets	8,475	11,763
Other operating lease assets	1,210	1,503
Other non-current assets	7,598	4,131
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	438,431	396,935
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	271,682	263,496
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	42,357	42,020
Operating Segments [Member] | Brazil [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	62,898	49,967
Operating Segments [Member] | Asia [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	61,494	41,452
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	62,460	48,600
Other PP&E	22,036	23,676
Other non-current assets	$ 4,235	$ 3,448