Mo. Rev. Stat. § 441.160: Executor or administrator of tenant for life may recover rents.

The executors or administrators of any tenant for life, who shall have demised any lands or tenements so held, and shall die on or before the day when any rent on such demise shall become payable, may recover:

(1) If such tenant for life die on the day, the whole rent;

(2) If he die before the day, such proportion of the rent as shall have accrued before his death.