SEGMENT INFORMATION - Reconciliation of Adjusted EBITDA to Net Income (Details) - USD ($) $ in Thousands	3 Months Ended	12 Months Ended
	Mar. 31, 2020	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Reconciliation Of Adjusted EBITDA To Net Income [Abstract]
Adjusted EBITDA		$ 203,080	$ 220,872	$ 255,114
Non-Operating Income and Expenses [Abstract]
Acquisition costs		(3,844)	(10,872)	(10,918)
ERP integration costs		(2,296)	(7,508)	(10,864)
Strategic initiatives and other charges		(33,799)	(13,449)	(5,266)
Legal matter reserve		(10,566)	0	0
Non-recurring / incremental COVID-19 costs		(4,655)	0	0
Goodwill write-downs		(90,408)	(77,572)	0
Net realized gains (losses) on divestitures and asset dispositions:
Gain (loss) on sale of ownership interests in a subsidiary		11,208	(6,469)	0
Realized (loss) gain on cost-method investments		0	(4,731)	3,771
Net gains from the sale of buildings and vacant properties		0	7,347	0
Joint Venture depreciation, amortization, interest expense and other charges		(4,732)	(1,514)	0
Stock-based compensation		(8,096)	(7,729)	(13,460)
Non-service pension and postretirement expense		(7,789)	(3,802)	(5,723)
Depreciation and amortization		(119,058)	(90,793)	(76,974)
Interest expense		(34,885)	(40,962)	(37,427)
Net loss attributable to noncontrolling interests		(497)	(901)	(260)
(Loss) income before income taxes		(106,337)	(38,083)	97,993
Income tax benefit (provision)		18,685	(806)	9,118
Net (loss) income		(87,652)	(38,889)	107,111
SGK Brand Solutions
Non-Operating Income and Expenses [Abstract]
Goodwill write-downs	$ (90,408)		(77,572)
Net realized gains (losses) on divestitures and asset dispositions:
Acquisition costs, ERP integration costs, and strategic initiatives and other charges		13,990	8,903	11,044
Memorialization
Non-Operating Income and Expenses [Abstract]
Goodwill write-downs		0	0
Net realized gains (losses) on divestitures and asset dispositions:
Acquisition costs, ERP integration costs, and strategic initiatives and other charges			2,696	1,430
Industrial Technologies
Net realized gains (losses) on divestitures and asset dispositions:
Acquisition costs, ERP integration costs, and strategic initiatives and other charges		268	3,073	613
Operating Segments | SGK Brand Solutions
Reconciliation Of Adjusted EBITDA To Net Income [Abstract]
Adjusted EBITDA		90,644	119,493	150,233
Net realized gains (losses) on divestitures and asset dispositions:
Net gains from the sale of buildings and vacant properties		(915)
Depreciation and amortization		(87,597)	(59,684)	(46,300)
Operating Segments | Memorialization
Reconciliation Of Adjusted EBITDA To Net Income [Abstract]
Adjusted EBITDA		146,285	134,286	145,487
Net realized gains (losses) on divestitures and asset dispositions:
Net gains from the sale of buildings and vacant properties		(401)
Depreciation and amortization		(20,527)	(19,731)	(20,005)
Operating Segments | Industrial Technologies
Reconciliation Of Adjusted EBITDA To Net Income [Abstract]
Adjusted EBITDA		22,753	24,082	25,864
Net realized gains (losses) on divestitures and asset dispositions:
Net gains from the sale of buildings and vacant properties		8,663
Depreciation and amortization		(5,771)	(6,195)	(5,796)
Corporate, Non-Segment
Reconciliation Of Adjusted EBITDA To Net Income [Abstract]
Adjusted EBITDA		(56,602)	(56,989)	(66,470)
Net realized gains (losses) on divestitures and asset dispositions:
Depreciation and amortization		(5,163)	(5,183)	(4,873)
Acquisition costs, ERP integration costs, and strategic initiatives and other charges		$ 22,985	$ 19,853	$ 13,961