if prostitute is beat do police jail the prostitute?

While not condoning... which would be the pimp's job to handle, and trust me, that's far worse than what the police would do.
Except where prostitution is legal, of course. And except where prostitutes work without a pimp or something, and just go report it to the police, because they don't give a frigging receipt so there's no way for the beater to prove they were a prostitute.