I had a little cat once that I adopted, he had one very badly deformed leg. He did well for a couple years but then suddenly he started peeing everywhere, at first I was mad, thought he was marking his territory etc. But then I watched him and realize that he was going and didn't even really know it. he was not positioned like he had to P it would just spray out no matter what position he was in or what he was doing. could this be happening with your cat with the stool?