Green’s Dictionary of Slang

to shoplift, to steal.

1863		Criminal Life (NY) 19 Dec. n.p.: [I]nstead of bumming round Moses for his Medford, hash, and chance to fish wipes out of his customers’ pockets.
1952		(con. 1948) G. Mandel Flee the Angry Strangers 138: In October. When you went fishing for a coat.
1968		J. Colebrook Cross of Lassitude 101: The termites of the life [...] who ‘heel’ and ‘boost’ in stores, who extract bundles of notes from banks by means of skillful ‘fishing’.