Moving out before the lease ends
If you move out before the end of the lease, the landlord may be able to hold you responsible for the rent that becomes due until the apartment or house is rented again, or until the lease ends.
For example, if you move out during July and your lease ends on October 31, you could be held responsible for the rents of August, September, and October. But if another tenant moves in on September 1, then the landlord may sue you only for August’s rent. This does not apply if the landlord agrees in writing to let you move before the lease ends.
If a tenant moves out before the lease ends, the landlord must try to re-rent the apartment. This means that in order to recover rent for the months left on the lease, the landlord must prove that he or she tried to find another tenant but could not. The landlord must show, for example, that he or she immediately began advertising the apartment and interviewing tenants. Cite: Sommer v. Kridel, 74 N.J. 446 (1977).