When an action commenced within the time prescribed by law shall abate by reason of the death of the plaintiff, if the right of action survived to his representatives, his executor or administrator may, within one year after such death, commence a new action, if the cause of such action would otherwise survive; and if any action so commenced by an executor or administrator abate by the death of the plaintiff, a new action may be commenced by the administrator of the same estate, at any time within one year after such abatement; or, if no executor or administrator be appointed within that time, then within one year after letters testamentary or of administration shall have been granted to him.