You would request a stay either in the eviction proceeding; or in the Article 78 proceeding. Separately, below are the requirements for a family member to stay in the apartment. We can discuss more if you want to do so.
(p) Occupancy rights of family members. (1) The rights of family members of a tenant/cooperator who have requested to remain as the lawful tenant/cooperator are governed by policies and procedures set forth in this subdivision, except in those instances where this subdivision is preempted by the rules or regulations of other federal, state or city programs. (2) As used in this subdivision the following definitions shall apply: (i) "Tenant/Cooperator" shall mean any person named on a lease as a lessee or who is a party to a rental agreement or proprietary lease and obligated to pay rent or carrying charges for the use or occupancy of an apartment. (ii) "Family member" shall mean: (A) a husband, wife, son, daughter, stepson, stepdaughter, father, mother, stepfather, stepmother, brother, sister, nephew, niece, uncle, aunt, grandfather, grandmother, grandson, granddaughter, father-inlaw, mother-in-law, son-in-law, or daughter-in-law of the tenant/cooperator. (B) Any other person residing with the tenant/cooperator in the apartment as a primary residence who can prove emotional and financial commitment and interdependence between such person and the tenant/cooperator. Although no single factor shall be determinative, evidence which is to be considered in determining whether such emotional and financial commitment and interdependence existed shall be the income affidavit filed by the tenant/cooperator for the apartment and other evidence which may include, without limitation, the following factors: (a) longevity of the relationship; (b) sharing of or relying upon each other for payment of household or family expenses, and/or other common necessities of life; (c) intermingling of finances as evidenced by, among other things, joint ownership of bank accounts, personal and real property, credit cards, loan obligations, sharing a household budget for purposes of receiving government benefits, etc.; (d) engaging in family activities by jointly attending family functions, holidays and celebrations, social and recreational activities, etc.; (e) formalizing of legal obligations, intentions, and responsibilities to each other by such means as executing wills naming each other as executor and/or beneficiary, granting each other a power of attorney and/or conferring upon each other authority to make health care decisions each for the other, entering into a personal relationship contract, registering a domestic partnership pursuant to Executive Order No. 48, dated January 7, 1993 or Local Law No. 27 of 1998, serving as a representative payee for purposes of public benefits, or other such formalizations; (f) holding themselves out as family members to other family members, friends, members of the community or religious institutions, or society in general, through their words or actions; 11 (g) regularly performing family functions, such as caring for each other or each other's extended family members, and/or relying upon each other for daily family services; (h) engaging in other patterns of behavior, or other action which evidences the intention of creating a long-term, emotionally committed relationship. In no event shall evidence of a sexual relationship between such persons be required or considered.