I was in a similar situation.
Bought a not livable house on large lot ($600k). Had a displaced tenant .. who owned an RV. I offered him the lot as a place to store his RV. We signed a "storage agreement" for $1000/mo. Which is not much on a $600k investment. It was supposed to be short-term until we got the map recorded and ready for demolition.
Well, the guy hooked up his RV, and started to fix up the house (without telling me)
One day, we got an environmental report done which included interior photos.
I could not believe my eyes. The bath had now a toilet again, the missing backdoor was installed, kitchen cabinets etc etc
He lived in a $3000/mo house and paid me only $1000 !
I raised his rent to $1200 :-)
I did not think it would be ethical to ask for market rent.
To those who think the guy won't pay or harass me.. he always pays by the 3rd, cash deposit in our bank account, never a phone call.. in.. a too long time!!!
Yeah :-( we bought the property in 2012, and still wrestling with the city.. demolition may not happen in 2017 either.
Property has appreciated $400k+, but as a rental, it looks bad on the P&L sheet.