So what if his copy of the contract was burned? Isn't it a given that each person should hold on to a copy signed of the contract? If I were her, I would be like: don't worry, mine is safe.
@Yabaibunni if you didn't sleep for three 3 days you go insane, imagine what like an entire life with no sleep will do. I don't think it has to do something with his interest in her, at least not at first. But more with the fact she would be the only person to let him rest. He is probably insane and needs treatment if we go after our standards, well, disregarding the fact that with absolutely no wink of a sleep he wouldnt even last that long.
If the contract burns then the contract is invalid and she would no longer be beholden to uphold her end of it either. I feel the story will use it to say she is forced to stay, but in reality she'd be free to leave.