It depends on your lease contract. More than likely your landlord will report to credit agencies that you have defaulted on your lease and you will subsequently have a huge ding on your credit score...
If you signed, the lease is binding. You don't have to move in, but you do have to pay the rent. The landlord has an obligation to try to rent the place, but until he does, you have to pay.
Usually when you find a suitable replacement for the remainder of your term on your lease you may leave the apartment. Sometimes though some owners require that they get approved like you do and...
If you have a month-to-month tenancy, either party can terminate the contract with at least a full month's notice. So, in January, the landlord can tell the tenant that if they want to be there March...