Legal Question in Credit and Debt Law in Texas

Re: Serving of a summons

They might give up and drop the matter.

But it is not likely. What will probably happen is that the process server will prepare an affidavit stating that he/she has exercised due diligence in attempting to serve you but has been unsuccessful. With that affidavit, and a motion from the plaintiff, the court will allow them to post the notice on the courthouse door, or a local newspaper. When you do not respond to that notice (which you will probably never see), the court will grant a default judgment to the plaintiff in an amount equal to everything that he/she can substantiate.

If you want to avoid the judgment against you, you should accept the papers, file an answer and attempt to resolve the dispute.