Dear New York Tenant:
No. Not usually. Landlord generally recognize the lease obligation that the security deposit is held in trust for the tenant for the duration of the tenancy, and that the landlord is compelled by the lease to return the entire amount held in trust, to the tenant, upon the tenant's moving out, and subject to assessing damage to the premises, beyond ordinary wear and tear, and in the event of damage, applying the security to the repair of the damage, and refunding the balance if any, at that time, to the tenant.
If the landlord somehow may invade the security for rent, then the landlord loses the ready and at hand security that the tenant has a fund on deposit for repair of damage to the rented premises.
A New York landlord is not required in ordinary circumstances to pro-rate rent. In New York, the rent is always due in full for the entire month, on the rent due date, even when the tenant moves out mid-month.
Your landlord may agree with you to refund a portion of the rent for October 2013, but New York law, does not compel that he do so. If you have had a cordial relationship, there is no harm in making the request, but ordinarily, a landlord will take the entire month rather than lose income for the month.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
Generally a security deposit is to compensate the landlord for damage not to pay rent. If the landlord agrees it's okay.
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I agree with the previous answers and if you can convince the landlord that is a good idea maybe.
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