Is there carpeting in the closet? If so you need to pull it up, cut out the pad and throw it away! Go to Menards and buy new pad. While the pad is out, look at the floor. If it is plywood and wet, the best way is to cut the wood out and replace it. You do not need to be very neat as it is covered by carpet. If it is hardwood then I would coat it with poly.
While the carpeting is pulled up treat the backside of the carpeting with the enzyme treatment. Do this several times. When done scrub it with a solution of vinegar and water as this will chemically react with the urine. You will then lay down new pad, new tack strips and hire someone to stretch carpeting.
Then when all done, take the cat down to the range and try out your AR-15 on a moving target! It is a fast paced shoot the whole family will surely love!