This is a theoretical question strictly for my own enlightenment. I like to learn odd things. :)

I know that the general rule of the law is that you have to return the property in the same condition that you got it. And that a tenant may be required to pay the landlord to undo any unapproved "improvements" (adding a deck, say). Does the landlord have to actually undo the improvement after getting that money? Or can they take the money and keep the improvement? I know that if you are in a car accident, the owner of the car doesn't have to use the money to fix damages, and was wondering if the same thing applied here. Or would the law consider that unlawful enrichment?

I am sory you have not gotten any answer.

The first thing to realise is that each state in the US has its own real estate law. So it may well be in writing somewhere. In my state I do not believe there is any written requirement that this be done.