Dear I figured it was good to know:
TV cannot tell you all you need to know. In New York a legal tenant may only be legally evicted by a judgment made by a judge in a court of competent jurisdiction.
In no circumstance, may a tenant (any person in occupancy of premises for at least 30 days) be evicted without a court proceeding. The nature of the proceeding is driven by the style of "breach" claimed by the landlord. For a proceeding grounded upon a default in the payment of rent, a landlord must as a precondition make a rent demand upon upon the tenant, and if the tenant's rent default continue beyond the stated time in the demand to pay, the landlord starts a nonpayment summary proceeding. In a nonpayment case, the tenant may end the case by paying the rent, take the case to a trial, and still keep his home even if he loses the case, by paying the amount of the money judgment (before a warrant of eviction is issued) and even later if granted permission by the judge via an order to show cause, or the landlord can choose to end the case and take the money and cancel the warrant. If the tenant does not pay and no extensions to pay are granted or sought, the tenant can be evicted only by a marshal in the City of New York and outside the city of New York by a County Sheriff or deputy Sheriff. Even after a full and legal eviction, the court retains jurisdiction to the extent that it may restore a tenant to possession (if there is no new tenant) on grounds that establish a meritorious defense and a reasonable excuse to vacate the tenant's default.
The other most common eviction proceeding is the holdover summary proceeding. In that case, also started in most instances by service of mandatory pre-lawsuit notices, a landlord claims a tenant's lease was terminated on some fault ground and the tenant did not correct the default before termination of the tenancy, or the tenant's lease ended by its own terms and the tenant did not move out, or the tenant engaged in objectionable conduct (the court must determine whether the claimed conduct is really objectionable and if not, the landlord's case ends), or the landlord terminated by a proper notice a tenancy without a current lease and the tenant did not move out. In all these types of cases, if the landlord wins and in case of a win based on a lease default the tenant does not cure after the landlord's win, the landlord is allowed to gain back possession after the final judgment by a marshal or sheriff executing the warrant of eviction.
All of these legal eviction cases are by court proceedings. If a landlord chooses to skip the legal process for some reason (the landlord does not like courts, lawyers judges or does not want its business out in public) then if a tenant would take money to give up the home, the landlord can avoid court. Often that evasion of the legal process makes no sense at all, because the landlord will gain back possession if legally entitled to possession for far less money than the landlord would need to pay an attorney to successfully prosecute his lawsuit to a final judgment.
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.