I believe it varies state to state (assuming you're in the US). So, I would read up on the landlord/tenant laws in the state of the rental. In my case, the tenants were on the hook for the remainder of the lease, but as a property manager/landlord I was obligated to put forth reasonable effort to find a replacement tenant. I also asked the tenant if they had anyone they'd recommend who was looking to rent the place, as it was in their best interest to also have a replacement tenant in place so they didn't pay for a place they weren't living in anymore. It worked out, they recommended an individual and they ended up in the place a day after they left.