Green’s Dictionary of Slang

1. hopeless, finished, with no chance.

1925		C. Hume Cruel Fellowship 210: I’m feeling frightfully sunk.
1932		Quad-City Times (Davenport, IA) 6 Apr. 2/1: ‘Don’t every think I’m nerts or I’ll go sunk’.
1934		Wodehouse Right Ho, Jeeves 1: It’s a thing you don’t want to go wrong over, because one false step and you’re sunk.
1939		J. Weidman What’s In It For Me? 333: If their wife gets sick or if they have a baby, they’re sunk.
1945		G. Fairlie Capt. Bulldog Drummond 197: Algy can’t go back because he’s sunk [...] the moment Irma Peterson sets eyes on him.
1959		W. Brown Teen-Age Mafia 122: If Whitey had abandoned them without any wheels they’d be sunk.
1969		‘Iceberg Slim’ Pimp 254: I would be sunk if there was a routine cell-house shakedown.
1975		‘P.B. Yuill’ Hazell and the Three-card Trick (1977) 179: If the law gives me a spin I’m sunk, in I?
2018		W. Kramer Hard Stuff 16: I knew I was sunk, but maybe this [i.e. religion] was a way out.

2. (Aus. prison) found guilty in court.

1990

Tupper & Wortley Aus. Prison Sl. Gloss. 🌐 Sunk. Found guilty.