If filing for divorce, what happens if the spouse being served cannot be found or refuses to sign?
When a spouse refuses to sign divorce papers, the filing spouse can get what is known as a "divorce by default". And  if the filing spouse cannot locate the other spouse they can serve notice of the legal proceedings by something known as a "service by publication" and then file for a default divorce.
The way it all works is as follows. Before any legal action can be taken against a person, they must be given an opportunity to appear in court and tell their side. Therefore, they must be given "notice" of the action. "Service by publication" allows a spouse to be served notice of a divorce action via a notice in a newspaper. The filing spouse i.e. "petitioner" must make a diligent effort to search for their absent spouse i.e. "respondent". Once they have presented proof to a judge that they made good faith efforts to find their missing spouse, the petitioner will be allowed to serve the repondent by publishing notice of the divorce in a newspaper instead of the more usual method of personal service. The respondent will then typically have 30-60 days to file an "answer". If they fail to do so, the petitioner can file a request to enter a "divorce by default". Generally, it is granted upon the terms requested by the petitioner, although the respondent is given a certain period of time in which they can appeal.
At this point you should consult directly with a divorce attorney in your area. They can best advise you of your rights/responsibilities under your state law.