The short answer is yes, but there are some limitations.

First, though, you need to make certain that Missouri has the jurisdiction (power) to dissolve your marriage.   You must have resided in Missouri (“resided” means lived in Missouri with the intent to remain) for the ninety days just before the Petition for Dissolution of Marriage (divorce) is filed.

Ordinarily, the person who did not file the case (the Respondent) receives the divorce papers by being handed them by a Sheriff or a person appointed by the Court to deliver them (a Special Process Server).  Where the person who filed the papers (the Petitioner) does not know where the Respondent may be found, service may be done by publishing a notice in an approved newspaper.  The judge must approve the so-called service by publication and in order to show that service by publication is appropriate, the Petitioner must show a diligent attempt to locate the Respondent: these attempts include asking family, friends, landlords and employers; the Social Security Office and FaceBook.  The Judge will rarely require the hiring of a private investigator (in over 30 years of doing family law, I have not seen or heard of this, but I think it is a possibility).

There are severe limits on what the judge can do in a divorce when service was by publication:  the marriage may be dissolved. The maiden or former name of the
Petitioner may be restored, the custody of children who have lived in Missouri for the six months just before the Petition was filed may awarded so long as there is no other legal proceeding pending concerning custody is pending and no one who is not part of the divorce has custody or claims the right to custody of any of the children and dividing any property located in Missouri, The judge can award property that is located un Missouri,

When service is by publication, the Judge cannot order the Respondent to pay money whether for a debt or to equalize property division or even for maintenance (spousal support).