Can a buyer who bought a house walk away after closing?

I rented out my house for 18 months with the buyers. They were supposed to buy the property after 12 months but didn't. They purchased the house with the agreement between him and I via a handshake that I would give him money under the table after closing since the mortgage companies wouldnt give it to him during closing. We closed 29 days into the month and they never paid the monthly rent. Since they never paid the rent, I believe that my payoff balance went up because I was charged nearly $1400 in interest charges because there was no monthly payment made. Since I am giving them back money, I am going to take that out of the funds we agreed upon. I tried avoiding the situation all month long and explained the situation well before closing and now that I am acting on it, they are upset and want me to eat that $1400. Now they are trying to say I owe for some fixes on the house that was never addressed before. Can they get upset and walk away from the deal after we closed on the house? they have lived in it since early 07.