As Florida family law attorney Christine Bauer points out on her Florida Divorce & Family Law Blog, divorce and family issues have a lot of intersecting areas of law such as real estate, bankruptcy, and immigration. Immigration issues can complicate a divorce, and cause much stress for the dependent spouse about their status in the U.S. Regarding H-4 visas, Attorney Bauer writes:

An H-4 visa is a dependent/spouse Visa that is issued when your spouse has a H-1B Visa. You cannot work with an H-4 visa but you are allowed to remain in the United States with your spouse. The H-4 visa is valid until it expires, and will also terminate when your divorce is finalized. It will remain in effect during your separation period, but upon your final divorce decree, it will terminate. Therefore, you must file paperwork to change your status and request a new visa with a new classification before the finalization of your divorce. If you do not do this, you can possibly be deported or required to leave the country on your own accord.

For more information on immigration issues, the U.S. Citizenship and Immigration Services has an extensive, is somewhat complicated to maneuver, website. Additionally, contacting a knowledgeable immigration attorney can help provide you with information and protect your immigration status through the divorce process.