Yes, both tenants are still responsible for the terms of the lease, even if 1 of them moves out. That's assuming that both Ts signed the original lease with you. If only 1 signed the lease, then that's the only person who is responsible for the lease, unless they got married after the lease was signed. Then the uniting in marriage automatically assumes they are both responsible for the lease. All paperwork moving forward, should have both names on it.