Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Dec. 26, 2021	Dec. 27, 2020	Dec. 26, 2021	Dec. 27, 2020
Segment Reporting Information [Line Items]
Net sales	$ 201,410	$ 162,776	$ 397,402	$ 304,281
Cost of sales	184,520	136,842	354,415	263,786
Gross profit	16,890	25,934	42,987	40,495
Segment depreciation expense	5,422	5,393	10,880	10,832
Segment Profit	22,312	31,327	53,867	51,327
Polyester [Member]
Segment Reporting Information [Line Items]
Net sales	92,418	76,696	181,885	145,772
Cost of sales	91,978	65,801	173,151	130,245
Gross profit	440	10,895	8,734	15,527
Segment depreciation expense	4,544	4,470	9,026	8,873
Segment Profit	4,984	15,365	17,760	24,400
Asia [Member]
Segment Reporting Information [Line Items]
Net sales	59,112	44,692	110,540	82,415
Cost of sales	50,601	38,164	95,058	71,309
Gross profit	8,511	6,528	15,482	11,106
Segment Profit	8,511	6,528	15,482	11,106
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales	27,601	24,253	61,339	46,859
Cost of sales	20,075	16,276	43,873	34,269
Gross profit	7,526	7,977	17,466	12,590
Segment depreciation expense	277	321	660	751
Segment Profit	7,803	8,298	18,126	13,341
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales	21,015	16,008	41,174	27,037
Cost of sales	20,829	15,613	40,262	25,977
Gross profit	186	395	912	1,060
Segment depreciation expense	444	438	879	880
Segment Profit	630	833	1,791	1,940
All Other [Member]
Segment Reporting Information [Line Items]
Net sales	1,264	1,127	2,464	2,198
Cost of sales	1,037	988	2,071	1,986
Gross profit	227	139	393	212
Segment depreciation expense	157	164	315	328
Segment Profit	$ 384	$ 303	$ 708	$ 540