Eviction?

In order to force you to move, the owner has to send you a notice and file an action in court to evict, you have to be served a legal notice, and given the opportunity to be heard in court, then it will be up to the court what happens.

What state do you live in?

The rules depend on where you live and what your written rental agreement say. If you have no written agreement, you would have to prove your right to live there, however, the owner of the house has a right to evict the renter, provided they follow all the procedures required.