Green’s Dictionary of Slang

(US Und.) any form of crime committed with the connivance of the victim; they will be able to collect the insurance.

1950		Goldin et al. DAUL 48/2: Consent job. An automobile theft inspired by the owner in order to collect the insurance.
1962		Ragen & Finston World’s Toughest Prison 795: consent job – A theft or arson committed with the consent of the owner or landlord in order to obtain insurance money. [Ibid.] 811: owner’s job – Same as ‘Consent Job’.