Pretty much every phone conversation, my mother insists that she's going to move out of there and back into an independent living situation. She is really unable to take care of herself, but if she succeeded in moving, I would want nothing to do with it. Can I walk away without any obligation?
Yet I remember a writer here saying her Mom was saying how unhappy she was at the nursing home, and on every visit it was high drama with the "take me home". Turns out the writer was going to the nursing home the same time every day, and one day she went at a different time of day and found her Mom in the common area with a group of other women enjoying herself. If I remember correctly, Mom was startled to see her daughter and was quite embarrassed. Oh the games our elders can play.
My loved one may have initially asked about going home while in regular AL, but I knew that she couldn't really do it, because she didn't know the address anymore, she couldn't dial a phone anymore, she had no cash or checks to pay a cab-plus a cab company wouldn't have known where to take her, and there was no family member who would take her anywhere. She had no means to do move out.
What I tried to do was to listen to her requests and promise to put it all in writing so the doctors and therapists could review her tests and progress and then we would make all the plans. She would forget this conversation each day, so it usually seemed to placate her. I told her she was in charge, but we had to complete paperwork and follow the doctor's orders so her insurance would pay.
My tip to you is to get used to hearing the delusional statements and demands. Let it go in one ear & out the other. You don't need to take them seriously. This is a new behavior to learn as a caregiver and it does feel weird. It seems like one day mom is a credible adult source of good information in your life, and the next she is not. It takes purposeful work on our part to shift into a different mode of interacting.
It doesn't sound to me like this is a real threat. It is a complaint and wishful thinking. She will be less able to act on these kinds of fantasies as time goes on. If you were her guardian you could prevent her from moving. But it doesn't seem to me that is a realistic possibility anyway. And I don't think that having guardianship would make it any more pleasant for you to hear this assertion over and over.
Mom has a delusion -- "I can live on my own." And like any delusion she is not going to be reasoned out of it with logic. Placate her and try to redirect her. "OK, Mom, I'll look into what it would take to get out of your contract here. By the way, I saw a big sign for the holiday party next week. Shall we pick out what you are going to wear? "
Walking away? That's tough, but if it's wrecking your life cut her loose. If you are her POA I would think you would want to settle her affairs as much as possible before you get out of her life.
I am dealing with that with my Dad who wants to bring my Mom home from long-term-care. He thinks he can help her walk upstairs to go to bed... in denial that my Mom is now bedridden. There is a point where I just want to throw my hands into the air and say "go for it" but you are on your own. Oh, my parents are in their 90's.