Thank you for your additional information.
They can try to sue you, but all you need to do is show the account records, since these homes are just interested in money and they are low life leaches who suck every dime they can get out of the poor patients under their care. However, if you prove that the money was used exactly as it was supposed to be used they can neither sue you or get you removed as PoA for your brother. CA has no family or sibling liability law and if none of you signed as personal guarantors this home is blowing smoke about suing you.
Unfortunately, if he does owe the money because the rent was not paid for a period of time, I am afraid they can indeed file to evict him for non-payment and he will have to go or the court would order him evicted. Thus, if you cannot get the money together, then I would suggest you get looking for a new place for him and based on their attitude and conduct in not working with your brother and you, it would probably be good to get him out of there anyhow.
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