Your sublease agreement was valid between you and the tenant. Since the term of that sublease expired on February 28, the tenant now has the right to bring a holdover proceeding against you. The part of your sublease that says there would be no holdover in any circumstances is not enforceable in court. If the tenant accepted your rent for March you may have grounds to have the case dismissed.
The above constitutes general information only and should not be considered legal advice.
Dear Brooklyn Subtenant:
Based upon your information, you would have a realistic chance to gain a court order dismissing the petition in the summary proceeding. You should consult an attorney to decide upon a strategy. You may answer the petition and state defenses. You may make a motion to dismiss the petition.
A petitioner in a summary proceeding must be entitled to "possession" of the leased premises, and the Court must find that right to possession is superior to the Respondent in possession.
A "former" tenant does not have a right to possession. It should not matter that your remaining in the apartment after the end of the sublease and lease caused the landlord to dun the former tenant for "rent", the proper lawsuit is by the landlord against you and the former tenant. The basis for the landlord's claim is that the tenant did not deliver vacant possession of the apartment at the end of the lease. But while the landlord would seem to have a legal right to maintain the proceeding, it would also seem the former tenant does not.
But for the moment, what is the point of forcing the landlord to start an eviction proceeding, if you succeed and dismiss the tenant's case? Based upon your information, the landlord would have a legitimate case against the tenant, and through that lawsuit, against you as well.
So consult with an attorney.
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.