Slowly this support obligation is being considered by divorce courts deciding if any or how much alimony (spousal support) should be paid as part of the divorce settlement. The foreign spouse has certain rights as well as their U.S Citizen Husband or Wife. The law in this area varies depending on which of the states in the U.S. a married couple is living. There are very few court decisions in this area but the situation is rapidly changing.
Both the husband and the wife need to think carefully and understand what their rights and obligations are. Getting a divorce a few years later may not release the U.S. Citizen or Green Card Sponsor from their obligations to their former spouse that they helped get a green card.
It is important for you to know that not only the green card holder is required by immigration law to notify the government (USCIS) within 10 days of changing their address but the U.S. Citizen who sponsors a person for a green card must also give the government notice of any change in their address as well during the 10 year obligation period.
Please contact a licensed Immigration attorney before you act on your specific situation. Immigration Laws and Federal Regulations are constantly changing and the general information provided can change over time.