If such tenant for life die on the day on which the rent was payable, the whole of such rent shall be so recovered but if such tenant for life die before such day a proportion of such rent, according to the time such tenant for life lived of the last year or quarter of a year, or other time in which the rent was growing due as aforesaid, making all just allowances, shall be so recovered; or a reasonable part thereof, respectively, shall be so recovered if the recovery of the whole or such portion thereof as aforesaid shall be unreasonable.