Our 90-year-old fell and fractured her femur. She does not believe she can get better so we can bring her home. She actually asked about accessing the "right to die" process. Which she does not qualify for and we explained that to her. She does not have a terminal disease.
I don't have the desire to live that long, nor do I want it if I'm not healthy.
But that motivation, that goal, that determination...I think that's what keeps people going. One of our doctors felt the same way and related a tale of a woman in her 100th decade, a woman who was always busy, always planning, and had such a positive attitude.
I don't know, though, how you can reach into your mother's psyche and inspire that desire to live, other than gathering information on others who've lived to be older and lived a full life and showing her that she can recover from a fracture and still live a fruitful life.
Maybe you can ask the therapists at rehab to share stories (without mentioning names, obviously) of others who've had fractures in their 90's and lived to recover and enjoy their lives. Honestly, even if they "fudged" or embellished the stories, it might be justified if it helps your mother.