How do you apply for a divorce from someone in another state?

My sister was married in New Mexico and then she and her husband moved to Illinois. About two and half years ago, he called her children in New Mexico and said if you don't come and get her, I will dump her on the streets of Chicago, IL. She had started showing some psychotic behavior. About a year later, he came out to NM with a trailer to live in. My sister was living with my husband and I. He went to the agencies to see who could help him with living expenses. When he went to the VA, they told him that as a convicted sex offender he needed to register a month before entering the state. He left the next day back to IL with out my sister. He said we could keep her. We don't know where he is or how to get a hold of him. She is now on disability living in an assisted living facility. She has become obsessed over finding him and is about to lose her placement there. She needs closure. Can we just put an ad in the paper?