In this case you have a tenant under market rent, who cannot find another place in a short time frame, who has a smoke and cat urine filled apartment.

But, it now appears the flooring is damaged from dog urin (this is the smell issue mentioned), instead of a plumbing leak.  

You got past the first big hurtle in real estate investment, signing up and reaching out in BiggerPockets.

My lease stipulates that the deposit will go to carpet replacement if the cat urinates on the carpet so it works for me.  

Jill,The puddle on the floor may not have come from the body or it may just be urine ... emptying of the bladder is not uncommon at death.  

The biggest hurtle there is the house being quite a ways away from my 40 hour job.

The home had years worth of clutter, plus a very strong pet urine smell, but structurally (except for leaking skylight), my contractor found the home to be solid. 

One wall/door frame actually has a warped door, rusted hinge and rot from the animal urine that has soaked it.

Soon enough, the condition of the properties will be so bad that not even people want to live there, except squatters and homeless people who will make the place smell like urine.

Your better option would be to say no to the new puppy before it urinates all over your unit and hope they decide to move out.If you are going to change the rules on the number of pets why bother having rules at all.