Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Mar. 26, 2017	Jun. 26, 2016
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 570,255	$ 525,442
Other current assets	4,705	4,790
Property, plant and equipment, net	201,516	185,101
Other non-current assets	536	4,909
Investments in unconsolidated affiliates	117,910	117,412
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	423,620	379,896
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	267,832	243,105
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	59,101	63,141
Operating Segments [Member] | International [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	96,687	73,650
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	14,912	6,674
Property, plant and equipment, net	13,688	16,597
Other non-current assets	125	4,863
Investments in unconsolidated affiliates	$ 117,910	$ 117,412