I have an older single friend who went out of town to visit family for a few months, and while she was gone she had a brain tumor diagnosed and has been told she has maybe 2 years to live. She isn't planning to come home, though she has a house here with a mortgage.

I genuinely want to help her out while she is still alive, and of course I would have an interest in acquiring her house after she dies (no family to pass it on to that I'm aware of). I have experience in short and medium term rentals, and feel I could fix up her house (would need some basic things like paint) and make a medium term rental. 

Would it be rude, or too much, to ask her about assuming her mortgage and home title in exchange for monthly proceeds of any profits until she dies? The house is sitting vacant right now (with her furniture) and needs someone to take care of it at least, and I would be willing to make the time to do everything to upkeep it and pay the bills, and forward her any profits for now, in exchange for me keeping them later (after her death).

I suppose you may say it depends on how much equity she has in the house... and I'm not sure the exact numbers but it's probably somewhere around 20k on a house that's worth around 100k. May be able to make $600/ month

I'm just not sure if that would be taking advantage too much. I don't really have any cash to pay upfront for it. I would rather assume the current mortgage and terms (low interest rate!) if possible. But don't know if I'm helping her out enough to justify what I'm asking for. ALSO how to word it asking her in the first place!