Once people are adults, you're absolved from any legal or financial responsibilities unless stated in a written contract.
I would assume if they are incapacitated and you wanted home care or around the clock palliative care, there would be someone at the hospital to take care of facilitating the financial compensation for all that. I would also assume that there are health programs that allow them to borrow money for this sort of thing.
When my grandfather went into a nursing home, we all pitched in because his insurance didn't cover his major expenses. It would be wise to look at health insurance plans that covered people in their old age and the specifics in the policy. Also, they should receive some type of government money when retired too so at the worst, I believe there would be some resources for access to minimal care. But thorough around the clock care at a private facility or home care is definitely a financial burden. It has nothing to do with your own finances. You'd have to make it work if you felt obligated to contribute financially. Or you could move in with them and take care of them like a PSW. If you are given power of attorney, you can do what you want with that money to support their care. But no, it never legally has to do with your own money. You're essentially individuals who happened to be related when everyone turns 18.
Good question. Hm.