That sucks, I had the same problem. I had to cancel moving out a couple times due to a delayed closing, and as a result my landlord enforced the long notice period dictated by state law - I paid through the first month I also paid my first mortgage payment.
Most state laws require that a landlord refund you prorated rent if the home is occupied before the end of your paid tenancy. I.E. you move in August and have to pay through October, and someone else moved in September 1, state law may disctate the landlord would be required to refund you September and October rent. While you can be forced to cover vacancies as described in your lease, the landlord also can't 'double-dip'.
