96 YO Mother fall questions

Hello and thank you for reading this message. Mom is in unusually good shape for her age. She's had a few falls over the last five years but has been very fortunate to really only have had some stitches and a couple bruises. She has started to walk with a cane but mostly walks around the house holding on to furniture, walls etc. Most of the house (she lives alone in her home), has no steps or tripping hazards. She stills drives regularly to PT, hairdresser and local store. She's been taking supplements for decades and takes BP and Thyroid meds for about ten years. She has a pacemaker. She cooks and eats a healthy diet. She had a minor stroke over ten years ago with no after effects. She's recently had issues with itching and dry skin and scalp. All in all she's amazing. A couple days ago she called and asked my wife and I to come help her get up from a fall in her kitchen.
We found her sitting on a hard tiled floor without any apparent injuries. There was a chair knocked over and some other things on the floor as she appeared to have been reaching for things. She weighs 97 lbs and it took all had to get her up without hurting her. I asked her what happened and she said she was standing at the table reading the mail and suddenly lost her balance and went straight down without hitting her head or anything else but she couldn't pick her self up. Most of the house is carpeted and a lot has throw rugs. She refuses to remove them. I think she likes the extra padding because she's fallen without having to tell us. I took the opportunity to address a number of falling while alone issues for the hundredth time. In the past I've noticed her balance has been getting worse and she refuses to use on of the several walkers around the house. I could go on about her risky lifestyle but why? Any suggestions to get her to carry one of the many phones at all times? And when should she be in assisted living before she falls and can't get up until I discover her unable to call for help?
Thanks again for reading.