Uncontested Divorce Now He Is Leaving to a Different Country?

I have been separated from my husband for almost 2 1/2 years all this time he has been in rehab for alcohol and drug issues. I finally found a good lawyer that has helped me get all the paperwork together, and he is wiling to sign, because after all he has never been there to help support our daughter. His aunt called me 2 days ago telling me that he is doing much worse. He lost his job, his car got stolen and his family is thinking about sending him off to Honduras (Central America) to another rehab center, which they claim is really good…anyway my main issue here is that he will be in a totally different country, so there is no way that my daugther will get any kind of child support $. How does it really work? Once he signs and he leaves?…What is next? Does my daughter just not receive anything? I am a bit confused and upset,because I cannot believe how some men cannot grow up and be responsible.
**I would like to add on that my soon to be ex husband is a resident, he is 31 years old**