Business Segment Information - Reconciliation of Segment Capital Expenditures to Consolidated Capital Expenditures (Details) - USD ($) $ in Thousands	12 Months Ended
	Jun. 27, 2021	Jun. 28, 2020	Jun. 30, 2019
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	$ 21,178	$ 18,509	$ 24,871
Operating Segments [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	20,180	16,355	20,521
Operating Segments [Member] | Polyester
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	15,325	13,714	17,291
Operating Segments [Member] | Nylon [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	728	249	624
Operating Segments [Member] | Brazil [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	3,461	2,332	2,574
Operating Segments [Member] | Asia [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	666	60	32
Corporate, Non-Segment [Member]
Segment Reporting Other Significant Reconciling Item [Line Items]
Capital expenditures	$ 998	$ 2,154	$ 4,350