Without the cooperation of your husband and the landlord only you can only be let out of liability for the rent as part of a divorce decree or separation agreement where your husband agrees to be solely liable for the rent. Otherwise, you are liable for the rent until the end of the lease term.
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Unfortunately, you are responsible for all of the terms and conditions of the lease you signed. If you leave and your husband fails to pay the rent, the landlord can go to court and possibly obtain a judgment against you for any rent due under the lease until either the end of the lease term or until the landlord rents to a new tenant.
You should consult a lawyer about both the lease issue and your separation from your husband.
Dear is there any way out of this issue?
You did not mention whether your husband is also a tenant along with you. If he is, and you leave due to the break up of a marriage, and he remained in the apartment, then he pay the rent on the apartment even though you are a co-tenant on the lease.
If you are the only tenant, your divorce attorney should have helped you work this out before you left your husband in the apartment while you had the legal obligation to pay the rent.
A tenant is allowed to "break" a lease on grounds of domestic violence as long a the tenant first obtained an order of protection. (New York Real Property Law Section 227 - C) If you have an order of protection, your lawyer may use this statute to assist you to be released as a tenant from the lease.
If you do not have an attorney, do not delay. You are ending a marriage and looking to escape from a lease.
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.