Even then, the odor goes away once the box is cleaned. I have had cats all my life. An odor coming FROM the litter box does not equate to carpet damage. You would have to let the box go a VERY long time without cleaning before the cat would resort to going outside the box.
If I had a rental home, and I allowed pets, I would require that the tenant provide proof that the cats had been spayed or neutered before I would approve them.

