A third model: “elderly peers”
My mother is now fairly old (she was born in 1937). Women in the family seem to have good genes, though, and she, her two sisters and some female cousins in their late 70s and early 80s are still quite formidable. They are also close to one another. So, my mum does have another option, which is to move in with her sisters. This is not as crazy as it might sound, because by pooling their forces they can hold out much longer than each one of them in isolation. Also, they would probably find this psychologically less disempowering than having to fall back on us, because they would help each other rather than being only on the receiving side.
Like in John’s description, my mother and her sisters and cousins are fiercely independent and would absolutely loathe becoming dependent, even on us.