Green’s Dictionary of Slang

fleece n.³

In phrases

wear the fleece (v.) [pun on SE fleece, the deceive, to cheat; ult. the Biblical story of Jacob and Esau]

to be cheated, deceived.

1832

Satirist (London) 25 Nov. 383/1: Crockey—[F]lats-are numberless, and fools — it would do your venerable heart good to witness the foolery. There is Kemp, for instance [...] Nick—What of him ? Crockey—He wears the fleece, as we say.