Business Segment Information - Reconciliation of Segment Capital Expenditures to Consolidated Capital Expenditures (Details) - USD ($) $ in Thousands	12 Months Ended
	Jun. 30, 2019	Jun. 24, 2018	Jun. 25, 2017
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	$ 24,871	$ 25,029	$ 33,190
Operating Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	20,521	21,070	31,423
Operating Segments [Member] | Polyester [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	17,291	16,605	25,442
Operating Segments [Member] | Nylon [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	624	1,366	1,247
Operating Segments [Member] | Brazil [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	2,574	3,063	4,540
Operating Segments [Member] | Asia [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	32	36	194
Corporate, Non-Segment [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	$ 4,350	$ 3,959	$ 1,767