If the plaintiff claims an estate for life only in the premises and pays a sum allowed to the defendant for improvements, he or his executor or administrator, at the termination of his estate, is entitled to receive of the remainderman or reversioner the value of such improvements as they then exist; and shall have a lien therefor on the premises as if they had been mortgaged for its payment, and may keep possession until it is paid. If the parties cannot agree on the existing value, it may be settled as in case of the redemption of mortgaged real estate.