It depends on the type of rug you use. We have a lot of successes removing pet odour completely from specific kinds of rugs and in most cases do significantly lighten them even if total odour removal is not possible.
Here’s the science bit: Pet urine can easily soak right through to the backing of a rug. The acidic stain becomes alkaline as it comes into contact with air. When this chemical reaction takes place, the urine transforms into urea crystals. These urea crystals remain in the backing where they are held by the glue that holds the rug together. It is the bacteria living off the urea crystals that cause the odour.