Green’s Dictionary of Slang

an untidy, sloppy or depressing person; thus droopy-drawered adj.

1932		(con. 1910s) J.T. Farrell Young Lonigan in Studs Lonigan (1936) 91: Studs Lonigan hadn’t even begun to pay that little droopy-drawers back yet.
1934		(con. 1920s) J.T. Farrell Young Manhood in Studs Lonigan (1936) 292: Sobered up, huh there, Droopy Drawers?
1949		(con. 1943–5) A. Murphy To Hell and Back (1950) 114: Can you guess what the kids called me? [...] Droopy-drawers.
1961		C. Himes Pinktoes (1989) 69: What other reason would Mamie have [...] if it wasn’t to trick that droopy-drawered bitch into her house?
1975		D. Nobbs Fall and Rise of Reginald Perrin (1976) 54: Hullo, droopy-drawers.
1989		H. Rawson Dict. of Invective (1991) 127: Even worse is the droopy drawers — a mess of a person who is about as much fun as a wet blanket.