N.M. Stat. § 37-2-9
When the plaintiff shall make an affidavit that the representatives of the defendant, or any of them, in whose name the action may be ordered to be revived, are nonresidents of the state, or have left the same to avoid the service of the order, or so concealed themselves that the order cannot be served upon them or that the names and residence of the heirs or devisees of the person against whom the action may be ordered to be revived, or some of them are unknown to the affiant, a notice may be published as provided in Chapter XCIV, notifying them to appear on a day therein named and show cause why the action should not be revived against them, and if sufficient cause be not shown to the contrary, the action shall stand revived.
NMS § 37-2-9