My Dad told me a funny story, which could have ended quite badly, where decent core stability would have saved a lot of angst.
He told me he fell in a ditch on the common and couldn’t get out, while cows snorted above his head and dribbled over him. He was aged 80 at the time, and was retrieving his model airplane which had flown into a field, when he fell into a roughly one metre high, narrow ditch, landing on his back. He tried to sit up but didn’t have the strength, and he couldn’t move his arms enough to enable him to turn around. There was nothing to grab onto. He said he was stuck for about half an hour, and the curious cows ambled over to see what the commotion was about. Finally he was able to wriggle onto his front and claw his way up and out. Would he have had a better chance of getting out of that ditch with better core condition? I think so.
I notice with my parents and clients that getting down to and up again from the floor can be very challenging. Improving core stability can help as it is integral to the task, whereby the whole body is required to move in a coordinated, multi-plane fashion. Your arms and legs can only be as strong as your core will allow. Try doing it yourself now; get down to and up from the floor, and see how you feel it in your abdominals.
Basic core exercises, as well as single leg strength moves like lunges and step ups, will be key to providing enough stability to transition to and from the floor. Practising the way you do it would also be helpful as an exercise in itself, and may prove useful in a fall situation.