I've been landed with the care of someone who has become unable to care for themselves and while talking with their family, I couldn't bring myself to ask if there's somewhere else they can go. But I can't keep doing this.
Be honest. Say you need to step back, and that "we" as a group need to find some other supporting pillars to jam under there to help the person in question.
If you burn out and can't help them, then everyone loses.