Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Dec. 27, 2020	Dec. 29, 2019	Dec. 27, 2020	Dec. 29, 2019
Segment Reporting Information [Line Items]
Net sales	$ 162,776	$ 169,511	$ 304,281	$ 349,460
Cost of sales	136,842	153,846	263,786	316,352
Gross profit	25,934	15,665	40,495	33,108
Segment depreciation expense	5,393	5,167	10,832	10,113
Segment Profit	31,327	20,832	51,327	43,221
Polyester [Member]
Segment Reporting Information [Line Items]
Net sales	76,696	82,750	145,772	171,445
Cost of sales	65,801	76,090	130,245	156,990
Gross profit	10,895	6,660	15,527	14,455
Segment depreciation expense	4,470	4,183	8,873	8,224
Segment Profit	15,365	10,843	24,400	22,679
Asia [Member]
Segment Reporting Information [Line Items]
Net sales	44,692	47,918	82,415	93,875
Cost of sales	38,164	42,401	71,309	84,076
Gross profit	6,528	5,517	11,106	9,799
Segment Profit	6,528	5,517	11,106	9,799
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales	24,253	20,862	46,859	45,034
Cost of sales	16,276	17,432	34,269	37,445
Gross profit	7,977	3,430	12,590	7,589
Segment depreciation expense	321	357	751	732
Segment Profit	8,298	3,787	13,341	8,321
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales	16,008	17,084	27,037	37,286
Cost of sales	15,613	17,038	25,977	36,062
Gross profit	395	46	1,060	1,224
Segment depreciation expense	438	503	880	994
Segment Profit	833	549	1,940	2,218
Other Segments [Member]
Segment Reporting Information [Line Items]
Net sales	1,127	897	2,198	1,820
Cost of sales	988	885	1,986	1,779
Gross profit	139	12	212	41
Segment depreciation expense	164	124	328	163
Segment Profit	$ 303	$ 136	$ 540	$ 204