It'll look like the glorified vinyl linoleum flooring it is, but hey, that's the price you pay for hands-off real estate investing, and lots of people like plastic everything in their lives.Ripping out a whole subfloor because of cat pee, as @Micah Mcarthur suggests, seems a bit much.

Could not really store anything in it that was not in plastic garbage cans.

Maybe I was a little too hard on it, MHs are a PITA, the repairs of cheap fixtures used, plastic bath tubs, RV water heaters, PVC plumbing that is sized too small, walls built over the carpet and flooring, losing AC units when they leave, window craks that get stripped out and leaky roofs.Now I know a lady who owns a park down at the lake and they are all older units.

Cardboard and plastic takes up a lot of negative space in the trash bins.

Step #1 - Put something (i.e. tarp, drop cloth, plastic sheeting, etc) down on the floor to help catch the mess and make for an easy cleanup.Step #2 - Fill a sprayer up with water and spray it on the popcorn ceiling. 

We've never offered cash for keys, but we have offered moving boxes, tape, 3-mil plastic bags, helpers with a truck, etc.

I would not worry about attaching a sheet of plastic to the studs, if that is what you mean by a vapor barrier.

What I would do is check your basement floor first by putting a 3 foot by 3 foot piece of clear plastic down on the floor first and tape around all corners.  

the little plastic tab on the leg was busted and a nail head protruded. 

That stuff is foam plastic?