What if I buy a house on a land contract and the previous owner refuses to move out and won't let me do anything with the property because her name is still on the deed?

What were the terms of the contract?

When you buy a property on a contract, the owner retains ownership until the contract is fulfilled. So they aren't the "previous owner". The owner can put in the contract that you can't make material changes. They can even put in the contract that you don't get possession until the contract is fulfilled.

Its unusual, but it can happen. If you signed such a contract then you are bound by it.

So you need to read the contract and understand its terms. If you feel the seller has not upheld their end of the contract, you can have it voided.