When the owner of real estate dies after a lien has been recorded, or dies pending an action brought against him or her to enforce a lien on such real estate, the action or lien shall not abate or be affected by the death of such owner, but the executor or administrator of the deceased shall be cited in and the action shall proceed to final judgment against the representative of the deceased defendant. Such real estate shall be holden for the amount due upon such judgment, with the cost of the copy of the record of the judgment and recording, as if it had been mortgaged for the payment of the same, in like manner as if the deceased defendant were alive. Such lien shall not be enforced to the diminution of a right or interest given by law to the surviving husband or wife, as the case may be, or to the children of such deceased person.