A relatively common scenario with rent-regulated leases involves two people living in an apartment, with both names on the lease. When the relationship ends, one moves out. What are their respective rights? First, the remaining occupant continues to retain rent-stabilized status, as long as he or she continues to pay the full rent, and comply with the other provisions of the lease. The party who vacates is still legally responsible for the rent, as long as both names are on the lease. It's possible to ask the landlord to change the lease to reflect the occupant's name only, but the landlord isn't required to. It may involve a negotiation in which the departing individual signs an agreement forgoing all rights to the apartment and a rent-stabilized tenancy.