Maybe you and the good sister could offer a promise to the bad sister to 'gift' her the money in the future in exchange for her giving up her claim to the money now? Probably would need to know the legalities, but perhaps something like paying for her future car maintenance and repair bills would gradually get her money to her without her risking whatever program she is on? Or if she doesn't have a car, an offer of letting her have a gift registry list on Amazon that you will buy the items to gift her for Xmas or something like that?
It would help to know what program she is afraid of losing because then you could find out the exact terms of it. I think some senior housing is only available to people with a limited net worth, and I can see that it would be a major hassle to lose an affordable living space due to a limited sum of money that would be rapidly eaten up by paying for full price housing, leaving her without either home or money.