we have an inherited tenant who is requesting that we remove the existing door on his bath tub so he can use a rod and curtain instead.

Last one was that the bath tub was "defective". 

As a tenant before I became a manager, I once had an overflowing bathtub situation that I couldn't manage - broken pipe and water wouldn't stop pouring out of the wall.  

Handyman put ladder in her bathtub to paint the ceiling above the tub, and didn't lay protection down first (tarp, towel) so the tub basin is scratched now.A/C unit in the bedroom was not installed properly years ago, and there were gaps you can see straight outside.  

restore or replace kitchen cabinets and countertops,new toilets and bathroom tile,new vanity sink,reglazed the bathtub or showers,etc.

She told me that the toilet doesn't flush and all the wastewater goes in the bathtub.

I had to hold back the giggles, though, when she stood in the hallway and said "There's no bathtub in the master bedroom."

Tenants will sometimes just use them stealthily.They can buy lint socks for the hose that will drain into the sink or bathtub. 

About 2 weeks ago, the facuet of the bath tub not working and water won't shut completely.

It's hard to say without a photo of the situation...but I will give a guess based on an experience I had years ago.In my case the drain overflow from the bathtub on the 2nd floor had settled away from the tub.