When a defendant cannot be found after diligent searching, the court may allow the plaintiff to serve notice by publishing it in a local newspaper of general circulation. The Affidavit of Service by Publication is signed by the publisher or an authorized agent of the newspaper, not the plaintiff.
It certifies that the legal notice (summons) was printed in the newspaper on specific dates, as required by court order (usually once a week for several weeks). This provides "constructive notice" to the public and the defendant, satisfying the legal requirement to attempt contact before a judgment is made. A copy of the actual newspaper clipping is usually attached to this affidavit.