I recently bought my mother who suffers from alzheimers and is really unsteady on her feet a pair of Velcro slippers, The Velcro fastening on the slippers have helped with her walking and she does not now walk out of them as she did with shop bought slippers.
We have very narrow windy cottage stairs in our house, which does mean that you go down slowly and hold the banister when you do, nevertheless I always wear solid composite soled mules walking round the house. Slippers, flipflops, or any soft soled footwear are too soft and bendy to be safe.