Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Dec. 27, 2020	Jun. 28, 2020
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 512,998	$ 474,162
Other current assets	10,282	11,763
Other operating lease assets	1,308	1,503
Other non-current assets	5,108	4,131
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	416,118	396,935
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	261,769	263,496
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	39,682	42,020
Operating Segments [Member] | Brazil [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	60,006	49,967
Operating Segments [Member] | Asia [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	54,661	41,452
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	68,900	48,600
Other PP&E	22,687	23,676
Other non-current assets	$ 3,985	$ 3,448