What are the stakes for my father’s house in California?

Hello! Please bear with me as I am in my early 20s and figuring this all out by myself since my early 70s father wants nothing to do with this.

My father bought a house in FULL a few years ago and put his girlfriend’s (at the time) name as a co owner. Which is terrible, I know. They soon broke up and he moved out. She has been living there and paying the property taxes/utilities. She recently asked him to pay this year for the property taxes and fix the roof. He declined. He is willing to sell but I doubt she would be since that is her home and she is very emotional/hardheaded. What are the options if it stays frozen like this and one of them passes first or the next step of legal action?

To give more context, she was abusive towards me at the end of their breakup. 2-3 years after the breakup, she called my father saying she wanted to give her half to me in her will. (I assume out of guilt.) He recommended a trust and she hung up. I know she did not do it but at least she’s conscious of what’s the right thing to do. (I say this fully knowing not to trust her word, obviously.) On this note, is a trust still on the table for something like this? Also can I go about that with as little contact as possible?