Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Mar. 25, 2018	Jun. 25, 2017
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 590,892	$ 571,503
Other current assets	7,178	6,468
Property, plant and equipment, net	203,713	203,388
Other non-current assets	3,781	2,771
Investments in unconsolidated affiliates	112,249	119,513
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	427,691	409,432
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	272,358	270,819
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	58,565	57,789
Operating Segments [Member] | International [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	96,768	80,824
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	30,861	27,375
Property, plant and equipment, net	16,177	14,904
Other non-current assets	3,914	279
Investments in unconsolidated affiliates	$ 112,249	$ 119,513