New Jersey Statutes Title 2A. Administration of Civil and Criminal Justice 2A § 42-12

When a tenant for life shall die before or on the day on which rent was reserved or made payable, upon a lease of real estate which determined on the death of the tenant for life, the executors or administrators of the tenant for life may in an action recover from the undertenant of the real estate, the whole, if the tenant for life dies on the day the same was made payable, or if before that day, then a proportion thereof, according to the time the life tenant lived in which the rent was growing due, making all just allowances or a proportional part thereof, respectively.