Father's third has just filed for divorce and he is 86. I am his only child and have an obligatory( at best) relationship with him for my adult life. He has always been very bitter, manipulative and claims he is clinically depressed. He has seen therapist for as long as I can remember and blames his mother ( and all women) for his feelings of inadequacy. He has a narcissistic personality and leaves me guilt ridden after every call or visit. He refuses to give anyone POA but I am seeing poor financial decisions being made. My morals prevent me from caring, but frequent involvement with him makes me physically/mentally sick and continued contact may hurt the relationship I have with my spouse and children. My husband and I have zero respect for him for many reasons.
You asked only about the legal or financial responsibility; were you thinking that you might have caregiving (i.e., housing, cleaning, cooking, etc.) responsibilities as well? If so, based on what you're written, I think it would be a disaster for you, particularly given his apparent chauvinistic attitude toward women.
I think it would be helpful if you investigate placement opportunities for him, but if he also refuses to delegate authority via a DPOA or medical proxy, I don't know how much you can be expected to do for someone who doesn't seem to trust on the legal or financial levels.
But do verify if there are filial responsibility laws in your state as the first step in your evaluation.
See: forbes/sites/northwesternmutual/2014/02/03/who-will-pay-for-moms-or-dads-nursing-home-bill-filial-support-laws-and-long-term-care/ for a brief overview of the concept. (if the link is removed, google "filial responsibility laws".)
If she did get guardianship, that might come into play. However, I haven't researched that many of the statutes and/or summaries of the law's provisions - that's a project for a rainy day when gardening season is over.
BTW, I like your "no holds barred" advice!
And you're soooo right about others opining without being asked (and generally without knowledge of a situation) about the son/daughter's handling of an elder's care.