Any action contemplated in sections 611.20 and 611.21 may be brought, or the court, on motion, may allow the action to be continued, by or against the legal representatives or successors in interest of the deceased. Such action shall be deemed a continuing one, and to have accrued to such representative or successor at the time it would have accrued to the deceased if the deceased had survived. If such is continued against the legal representative or successor in interest of the defendant, a notice shall be served as in case of original notices. If such an action by the deceased is allowed to be continued, then the court shall appoint a personal representative for the deceased as defined in section 633.3 or shall allow a successor under section 633.356 to continue the action.