What is the single-most-important consideration in determining whether a frail elder can remain at home? the number of chronic illnesses the availability of a caregiver the frailty of the individual the behavior of the individual?

I'm considered an elder. I have a wonderful caregiver (my wife) who has come to understand that the vows we took nearly 37 years ago have come to the worse part of "do you take this man for better or for worse, in sickness and in health ... " 

I could not remain where we are without her. For me the caregiver is the most important consideration, but I doubt very much that that is the answer you are looking for. 

The actual answer is the frailty of the individual. A close second is likely the number of chronic illnesses one has. 

They're all important and each could be argued on an individual basis. The number of chronic illnesses is not an issue if they are all in remission, which in an elder, is a very lucky state.

It really comes down to how well you can take care of yourself even on a limited basis. That's the deciding factor. Is your cancer leaving you alone even for a short time? Is your blood pressure controlled by medication? Have you accepted you condition whatever it is? Can you do anything to prevent your loved ones from worrying? Can you remember where you put your car keys? If you answer yes to most of them, you're frail, but you're good to go or to stay.