Eviction is a separate proceeding from seeking back rent. Eviction looks to settle only possession of the apartment; a landlord brings it to get rid of a tenant who doesn't pay, who damages the premises, who breaches the lease in some other way, etc.Because eviction is concerned only with possession, you generally cannot get money in the eviction proceeding, unless in a nonpayment case, the tenant brings the full amount owed and pays it, in which case you then can't evict them (if they pay up prior to eviction, they get to stay).You have a right to the back rent owed, but you would need to seek it in a separate lawsuit, though you may file that suit in small claims court, if the amount if underneath the small claims jurisdictional limit, in order to save on court and lawyer fees.