I've been through this 3x. Twice, did it Sue's way. Ran everything by my sister. I did almost all the caregiving for mom and dad but I kept it fair. It was heartbreaking when she see family items as junk and was just interested in what money could be made from the sale of things or in the really good stuff. We split it all 50/50. I can live with myself - I wonder how she lives with herself.
Last time with my mother in-law, sibling issues were rampent. Things disappeared but I got the house emptied out and stored (costs and labor all on us) until her death as break-ins in empty houses of the elderly is high and it did happen once before we emptied the house.
I real questions regarding the inability to see a senior's home if in a facility and being paid by the State. There should be a way to sell it and not keep the expenses going and maintence needs. I'd check that one with an Elder Law Attorney.
If a senior's mental capacity is in question for life's decisons or just financially, Conservatorship or Guardianship is what you need.
It is too late for several proactive steps that could have been done in both cases presented, though. For others, think in terms of creating a Will that includes a list of who gets what, even put post-its on the back of furniture/pictures/etc on who it goes too.
Because of what I went through, very similar to the above cases, I ended up creating an e-book for others to use to organize all assets and lists and even burial preferences, it is at www.thepracticalexpert.com. I'm not interested in selling but rather for people to plan ahead if they have elderly parents or relatives so that so many heart rednering and stressful situations can be avoided. Also the hardfeelings that linger long after.