Thank you.Seeds of Chaos kind of fits the bill a bit. The protagonist is a former hero named Rowan who has his fiance kidnapped and made to be a slave by the children of the demon he killed. They then force him to help them which he does to try to save her.
In Anera The Demon Tower the female protagonist fights monsters and prostitutes herself to try to save her best friend from being sold at auction.
There's also Third Crisis in which the protagonist is an agent named Vibe is trying to save her girlfriend from the clutches of an evil organization Peitho, which has basically taken over the world. Theres alot of content centering around the protagonist in this one though.
I hope you like some of these, they're not an exact match for what youre looking for though, there was another game I cant remember the name but it was an RPG where the protagonist had to make money by a deadline in various ways. If they didnt make enough money their sister who was captured would basically be used as a toy for the landlord. I'll try to find it in my game folder.
I've been trying to find a link for Beastkin Training on here but I haven't been able to find it. Have you seen a link?
Love and Corruption looks goodLove & Corruption (not a corruption game, i would never endorse anything unwholesome) has a route with Lisbeth (cat girl.. maybe 2 on the furry scale if an anime catgirl is a 1) who is a prostitute but hates working as one, and by the end of current gameplay when you become more famous/successful and have a place to live + the money to help her, you can save her from her situation.
Very cute, and as a bonus there's family raising stuff in the game and it's adorable!