Green’s Dictionary of Slang

(US) absolutely penniless.

1935		A.J. Pollock Und. Speaks n.p.: He went tapioca, he has lost all his money.
1963		A.S. Fleischman Venetian Blonde (2006) 244: I’d be right back where I started – Tap City. Tapioca. Broke.
1990		(con. 1930s–60s) H. Huncke Guilty of Everything (1998) 241: ‘I’m going to make a little money. Would you like to come along?’ I said, ‘Sure, I’m almost tapioca. Let’s go.’.