Business Segment Information - Reconciliation of Segment Total Assets to Consolidated Total Assets (Details) - USD ($) $ in Thousands	Jun. 25, 2017	Jun. 26, 2016	Jun. 28, 2015
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	$ 571,503	$ 525,442	$ 474,761
Other current assets	6,468	4,790
Property, plant and equipment, net	203,388	185,101
Other non-current assets	613	4,909
Investments in unconsolidated affiliates	119,513	117,412
Operating Segments [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	409,432	373,232	335,710
Operating Segments [Member] | Polyester [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	270,819	243,093	208,411
Operating Segments [Member] | Nylon [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	57,789	63,141	66,490
Operating Segments [Member] | International [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Total assets	80,824	66,998	60,809
Corporate, Non-Segment [Member]
Segment Reporting Asset Reconciling Item [Line Items]
Other current assets	27,375	13,337	6,892
Property, plant and equipment, net	14,904	16,597	13,544
Other non-current assets	279	4,864	4,714
Investments in unconsolidated affiliates	$ 119,513	$ 117,412	$ 113,901