If you can prove that the breached the contract by not complying with a term of the lease, such as repairs/maintenance, then you would not be responsible for remaining period of the lease.
If you can also show that the apartment was rerented, you would not be responsible for the rent after the date on which the new tenant moved in. This would be true whether or not they breached the lease. The legal term for this is "mitigation of damages".
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Attorney
Attorney and small business owner with 8 years experience in the general practice of law.