I am a co-owner of a house with my ex boyfriend in Arizona. He moved out without notice. He has an apartment and told me that he was just going to let the house foreclose. I cannot afford the mortgage on my own. I said I would just get roommates (which would be my mother) He told me no he wouldn't let me do that because he is a co-owner and would evict her. If he has established a new residence does he have the right to tell me (who is still living in the house) who can and can't move in?

He can not evict people you allow in, You can move her in with you if you want to.

He is still and will always be co owner until you buy him out.

He can't evict without both owners agreement. So he's making empty threats.

On the other hand, he will remain co-owner so if you sell he gets half the proceeds. So before you start putting more of your own money into this house I would suggest that you either refinance and buy him out or sell the house and take your share and buy another.