For most people who have obtained U.S. lawful permanent residence (a green card), their primary concern is to make sure they don't do anything to lose their status. However, some people find that, even after getting a U.S. green card, they would prefer to live somewhere else in the world. For example, after an immigrant has married a U.S. citizen, the couple might decide that both of them would enjoy living in and raising their children in the immigrant's home country.
In such cases, keeping the green card can be more trouble than it's worth, primarily because:
To deal with and clarify the situation, some people choose to surrender or give up their lawful permanent resident status. The method for doing this is by submitting State Department Form I-407. For more on the legal issues, see "Why Voluntarily Abandon Your Green Card? I-407 FAQ".
The best way to obtain Form I-407 is to go to the website of the U.S. embassy or consulate serving your home country, and search for "I-407." You'll find links to the website of your nearest consulate on usembassy.gov.
There is no need to advise anyone before you leave the United States. After leaving, however, you should file the Form I-407 at the U.S. embassy or consulate having jurisdiction over your place of residence abroad. Some embassies and consulates allow you to submit Form I-407 by mail.
There is no application fee for Form I-407. You must turn in your green card along with the Form I-407.
After you file, you will be interviewed by a U.S. consular officer who will want to confirm that your abandonment is willful and voluntary and that you understand the consequences of the abandonment. A copy of the Form I-407 will be returned to you as evidence of the abandonment of your lawful permanent resident status. The State Department asks that you keep a copy of the completed I-407 in your passport whenever you later travel to the United States.
If you are a long-term resident of the United States, meaning you were a U.S. lawful permanent resident during at least 8 of the prior 15 taxable years prior to giving up your permanent resident status, you must also take formal steps to advise the IRS of your relinquishment of residency. This involves filing a completed Form 8854 with the IRS. The form and instructions can be obtained on the "Instructions for Form 8854" page of the IRS website.
Once you abandon your lawful permanent resident status, you permanently lose all privileges associated with a U.S. green card -- you can't simply change your mind later and get your green card back. You will not be able to enter, live in, or work anywhere in the United States without getting a new entry visa or reapplying for a green card.
However abandonment of your lawful permanent resident status does not bar you from applying for lawful permanent resident status in the future. (You'll just have to go through the same long, complicated set of steps that you probably remember from last time.)