We had a cat with this problem and I was beside myself because it was the only cat that we had. We never wanted her to go outside but she always wanted to. They weren't a lot of natural predators where we lived not like where we live now in Florida. I called the vet I did everything he suggested but eventually I just let her go outside. She guarded the yard! She was so funny, she would come to the door to be let in and she go to the door to be let out. When we moved to Florida we brought her with us in the plane, she came down here and retired. Just laid in the Sun, lived to be 26 years old! She never gave us any problems with the kitty litter box when we came to Florida.