Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Sep. 27, 2020	Jun. 28, 2020
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 492,237	$ 474,162
Other current assets	9,760	11,763
Other operating lease assets	1,406	1,503
Other non-current assets	3,950	4,131
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	405,521	396,935
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	263,493	263,496
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	41,222	42,020
Operating Segments [Member] | Brazil [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	52,667	49,967
Operating Segments [Member] | Asia [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	48,139	41,452
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	58,549	48,600
Other PP&E	23,093	23,676
Other non-current assets	$ 3,668	$ 3,448