My mother is caring for another family's father who falls a lot. My sister and I are afraid one day he will fall and take our beautiful mother with him. What can we do?

My mother who is 87, and has been living on her own in our family home since my father died in 1992. She started seeing a man who is now 92, several years ago. Her "friend" is a lot of company to her, but his health has deteriorated to the point that she has become his caregiver. He has two sons who just let my mother continue fretting over him, taking him to doctor after doctor, finding him a place to stay when she goes on a trip, brushing his hair, setting up appointments for him, including having other caregivers into her home to bathe him, and give him physical therapy. It is exhausting for her, but she is a wonderful lady with a big heart who never complains, and would never never suggest putting him in a "home". My sister and I have talked to her about doing something else, but she just shrugs it off. We think his sons should step in and take care of their own father. My mother's quality of life is suffering. He falls a lot. Last night my mother had to call 911 again. My sister and I are afraid one day he will fall and take our beautiful mother with him. What can we do? My sister calls her sons sometimes when they don't take action, such as when my mother was recovering from breast cancer a few years ago, and needed rest. Please advise us on how to intervene appropriately, before our mother is hurt taking care of someone else who has a family!