mcem, I do think dealing with mental illness is very very hard to d, especially when combined - and caused by physical illness
Generally, I think it very much depends on the nature of the health problem, how far the ill person can continue to lead their normal life, what other support systems (partners) they have and who they need to care for (children)
Our only experience is of sudden looking after our daughter after she was seriously injured in a road accident. DH and I lived with her for two months after her (premature) discharge from hospital.
We stayed, usually only one of us at a time because DD preferred it that way, until she was physically able to manage her own life again; bathing and dressing, cooking and cleaning and was back behind the wheel. Then, when she thought she could cope unaided, in the nicest possibly way, she made it clear that she would like to have her house to herself again.
Her medical treatment continued for another 5 years, including further ops and we just played it by ear. She always wanted and needed us to stay for a few days when she had further operations and sometimes for other treatments and would ask for help when she needed it.
I think, we just have to be sensitive to what our adult children want us to do and not try to to do more than they want.