Sec. 18. If a life tenant who has demised any lands dies on or after the day on which rent is due and payable, the executor or administrator of the life tenant's estate may recover from the under tenant the whole rent due. If the life tenant dies before the day on which rent is due:
(1) the executor or administrator of the life tenant's estate may recover the proportion of rent that accrued before; and
(2) the remainderman may recover the proportion of rent that accrued after;
the life tenant's death.