Green’s Dictionary of Slang

1. to solicit, to work as a prostitute.

1846

Swell’s Night Guide 40: The French shicksters fight coakum better than our shakes; they do not lush nor scrap, and can sweeten a swell better; they are not so barefaced in their prossing.

2. (US) to be sexually promiscuous; to have sexual intercourse.

1961		T.I. Rubin In the Life 87: Lots of these legit married broads screw around anyway [...] They’re prossing like me, Doc, only with one guy instead of a hundred. [Ibid.] 112: Under the table, guy pops off and that’s it. They don’t go in for regular prossing.
1963		in T.I. Rubin Sweet Daddy 42: This one, that one, got a great big thought about prossing – you know, hustling.