When a tenant for life demises any lands and dies on or after the day when any rent becomes due and payable, his or her executor or administrator may recover from the subtenant the whole rent due, but if such tenant for life dies, before the day when any rent is to become due, his or her executor or administrator may recover the proportion of rent which accrued before his or her death, and the remainder man shall recover for the residue.
735 ILCS 5/9-217