So with the balloon experience in hand, maybe that smell isn’t stale, rather it has kept it’s odor fidelity all these years!

Smells and odors, especially urine. 

Residents who wish to be "grandfathered" and continue smoking will be allowed to do so; however, if odors from someone's smoking can be detected in another unit or common area, then the Board can permanently remove the "grandfathered" exception for that owner.  

Hire a company that has special services for pet staining and pet odor and deduct from the deposit at the end.In my opinion a pet fee does not cover damage to the property.  

We're looking at buying an ozone machine to help with odors after tenants vacate. 

About the only way I have been able to completely remove those odors are to:Remove old carpet and padding, remove existing window shades/curtains/blinds, paint walls, Change air filters and possibly have air ducts cleaned, pretty much anything porous enough to absorb odors will have to be removed for odors to be completely gone.  

I am turning a unit in Omaha with an inherited tenant whose unit contained, grease all over stoves and vents, cobwebs/dust on walls, really bad odor (cigarettes), blackened floors and shower.

We are just finishing up on demo and when removing insulation on the interior walls of the finished basement there is an overwhelming smell of mouse pee odor.  

You might want to paint the subfloor with kilz to seal in any odors-Install new flooring. 

You don't convince the tenant, she had unauthorized cats, and the cat pet caused the damages, are her expense,  You will never get the cat pee odor out, you may even have to get the sheetrock replaced about 2 feet up from the floors if the cat spray was that bad.after the sub floor is up, I would use Kilz and paint the joists before putting down new subfloor. and use kilz as primer before you do any painting.We flipped a cat pee house, had to remove the subfloors, and sheetrock for 2 feet from floor, the base molding, and door frames and doors the wood was so permeated with cat spray it was not an option to save.. we kilzed the entire area with this primer before painting..