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Business Segment Information - Reconciliations of Segment Gross Profit (Loss) to Consolidated Income Before Income Taxes (Details) - USD ($)
$ in Thousands
 3 Months Ended 12 Months Ended
Jun. 28, 2020
 [1]
Mar. 29, 2020
 [1]
Dec. 29, 2019
 [1]
Sep. 29, 2019
 [1]
Jun. 30, 2019
 [2]
Mar. 31, 2019
 [2]
Dec. 30, 2018
 [2]
Sep. 30, 2018
 [2]
Jun. 28, 2020
Jun. 28, 2020
Jun. 30, 2019
Jun. 24, 2018
Jun. 24, 2018
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]                          
Gross profit $ (9,451) $ 15,383 $ 15,665 $ 17,443 $ 18,342 $ 13,791 $ 14,156 $ 20,019 $ 39,040 $ 39,040 $ 66,308 $ 86,428  
Selling, general and administrative expenses                   43,814 52,690 56,077  
Provision (benefit) for bad debts                   1,739 308 (38)  
Other operating expense, net                   2,308 2,350 1,590  
Operating (loss) income                   (8,821) 10,960 28,799  
Interest income                   (722) (628) (560)  
Interest expense                   4,779 5,414 4,935  
Equity in loss (earnings) of unconsolidated affiliates                 477 477 (3,968) (5,787)  
Gain on sale of investment in unconsolidated affiliate                   (2,284)      
Impairment of investment in unconsolidated affiliate                 45,194 45,194      
Loss on extinguishment of debt                     131    
(Loss) income before income taxes                   (56,265) 10,011 30,211  
Polyester [Member]                          
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]                          
Gross profit                 12,088 12,088 23,819 33,194  
Nylon [Member]                          
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]                          
Gross profit                 (978) (978) 7,896 10,484  
Brazil [Member]                          
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]                          
Gross profit                 11,195 11,195 18,579 25,861  
Asia [Member]                          
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]                          
Gross profit                 16,683 16,683 15,700 16,620 $ 16,620
Other Segments [Member]                          
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]                          
Gross profit                 $ 52 $ 52 $ 314 $ 269  
[1] Gross loss for the fiscal quarter ended June 28, 2020 includes the adverse impact of lower fixed cost absorption in connection with the COVID-19 pandemic.
[2] Gross profit for the fiscal quarter ended December 30, 2018 includes the adverse impact of a raw material cost spike that could not be effectively offset with timely corresponding selling price increases. Gross profit for the fiscal quarters ended December 30, 2018 and March 31, 2019 includes the adverse impact of significant competitive pressure caused by elevated levels of polyester textured yarn imports.