The equivalent concept in English is "service by publication". When a defendant (in this case the "deudor") cannot be served process via normal channels, the court orders "notificación por edictos" (called "notification edictal" in your text), i.e., publicizing the fact that proceedings have been brought against the defendant, usually by posting it on court bulletin boards or publishing it in official gazettes, etc.

Your text indicates that "service by publication" cannot be used in a "proceso monitorio" (summary debt collection proceeding).

service by publication n.-- serving a summons or other legal document in a lawsuit on a defendant by publishing the document in an advertisement in a newspaper of general circulation. Service by publication is used to give "constructive notice" to a defendant who is intentionally absent, in hiding, unknown, and only when allowed by a judge's order based on a sworn declaration of the inability to find the defendant after "due diligence" (trying hard).
http://legal-dictionary.thefreedictionary.com/service by pub...