Green’s Dictionary of Slang

(US drugs) a period in jail, in order to withdraw compulsorily from drug addiction; also as v.

1969		R.R. Lingeman Drugs from A to Z (1970).
1973		E. Bunker No Beast So Fierce 223: If Willy was lucky [...] some anonymous bureaucrat or committee would order him a ‘dry out’, thirty to sixty days in jail.
1985		N. Pileggi Wiseguy (2001) 215: He was drying out and trying to get the bail reduced.