Can someone explain what happened with P?

Yes, they were.

...until Joe didn't trust P's judgment about the use of guns over the one debtor. She takes the gun from her after that case and basically chastises her for following her nature, which is one of violence, much as how Joe's is sexual. I don't think we're meant to know the exact details as even Joe doesn't, but it seems like the more she collected from Jerôme, the more she fell under his sway, much as Joe did when she was a young woman and they eventually became connected over their mutual disdain of Joe. How Jerôme came to realize P knew Joe is also up in the air, but it's easy to assume once he did, he filled her head with exaggerations of how he was a victim of her's while playing up his "innocence" and furthering P's hatred of her.

As for the climax, P, by that point, is completely under Jerôme's spell and completely hateful towards Joe as she sees him as an escape into a comfortable lifestyle, free of crime and free of Joe.

The relationship between Joe and P is like a reverse of the relationship between Joe and Seligman.

Joe takes P into her confidence and feigns an interest in her, but she's only using her for her own needs. Later Seligman will do the same to Joe.

You could argue that P loses her feelings for Joe once Joe confesses her intentions; that she was encouraged to care for P not because she loved her but because it was a good business decision. P says she doesn't care about this, but it's possibly becomes a seed of doubt that works towards turning her against Joe later in the film.