My ex-husband has not paid an type of support since 2009 and his whereabouts are unknown.
Family Law Attorney
If after attempting service at his last known address you may serve him via publication, so yes after following the required steps you should be able to accomplish this even though you may not know exactly where he is.
Please note that my response does not create an attorney client relationship, is general in nature and is not to be considered legal advice.
Criminal Defense Attorney
Yes, you can file a Petition with the court. However, the Court takes a TPR (Termination of Parental Rights) very seriously so I would highly recommend that you speak with an experienced family law attorney in detail about your case so that you can receive a step by step guideline on the allegations you must allege in the Petition and how to effectuate service on an individual whose whereabouts are unknown.