Why don't they last long after becoming bedridden?
Your body really isn't meant to stay horizontal 23+ hours/day, and that's what many elderly people are reduced to after a bad fall.
Bed sores develop very quickly, and an elderly immune system often simply isn't equipped to fight them. Gangrene and amputations are extremely common in end-of-life care.
For clarity, this sets in as the old body may still be slowly or practically unable to recover from the first event, the fall (e.g. a broken bone).
Elderly people frequently die because they get weak, then they fall and end up bedridden. At that point they don't last very long.