A landlord can file a holdover proceeding after the expiration of a lease. Payment of rent is not a solution.
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Dear can a tenant be evicted for no reason?
Unless the tenant is rent regulated, New York law does not require that the landlord have a reason for a decision to evict either at the end of a lease, or for a termination of a month to month tenancy. A tenant may defend against a termination of a month to month tenancy on a claim that the eviction proceeding is in the nature of a retaliation against the tenant for making complaints about the building or repairs, if the tenant could prove making those complaints within a six month-window before the landlord served the termination of tenancy notice.
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.