This is what I can gather. I think this is the chain of events:

These few episodes confirm what we were given a glance of in Higurashi ep 9 (non-kai). In that one, Teppei came to Satoko as well, and the beginning first few minutes of that arc showed Rina’s mutilated body in garbage bags. She had her nose cut off, intestines dragged out and had nails driven into each joint, Sonozaki execution style. (Or someone who wanted to make it seem like that.)

So same with this arc, she got ‘caught’ early on (it’s probably safe to assume she’s in garbage bags again now.)

So when she dies, Teppei has no where to go and no way to make money, so he takes over Satoko’s life.

If she doesn’t die, she goes on to make Rena and her dad miserable, it seems. But in that case she’s still working with Teppei and he doesn’t go to Satoko’s house. (But then Rina STILL ends up in pieces in a garbage bag courtesy of Rena. Some prostitutes have no luck I guess.)