A lease for a specific term does require you to pay to the end of the lease, whether you move out before that time or not. If the landlord has a new tenant who moves in before the end of the lease, then you would only be responsible to pay your pro-rata share of November's rent. The landlord has a duty to take reasonable steps to obtain a new tenant. Also, it depends on whether or not you paid last month's rent in addition to first month's rent when you rented the house. If you did, then that would suffice for November's rent, or any pro-rata portion of the rent you might owe. However, if you paid a security deposit at the beginning of the lease, and not last month's rent, then you need to pay the additional rent in accordance with the above guidelines. The security deposit is reserved for any damages that may lawfully be deducted from the deposit.