In Ohio, if you are in breach of the lease agreement, your landlord can file a forcible entry and detainer action (what most people think of as an eviction) in order to recover possession of the premises from you. The landlord can also file a second cause of action for money damages for the amounts due and owing under the lease agreement.
But the landlord must take steps to properly mitigate its damages (by trying to find another renter to take over your rental obligations as soon as possible). If you can show that the landlord is not attempting to mitigate damages, then that would be defense against any action for unpaid rent.
Whether your landlord will or will not do these things I don't know. Each landlord is different and has different policies and reasons for doing things. I can speak only in terms of possibilities, not probabilities.
