If parent with physical custody flees the country and leaves the non-custodial parent can child support be terminated?

My ex-wife has decided to leave (move out of) the US but is leaving the child with me. She does not want to break the law and knows she can't take the child out of the US. I am the non-custodial parent. What rights do I have? Can I stop the automatic child support payments as she will continue to get my money even though she no longer is caring for the child? Can I become the custodial parent due to abandonment?