After obtaining U.S. lawful permanent residence (a green card), the U.S. government expects you to actually live in the U.S. – and will consider your green card to have been abandoned if you make your home in another country, most often (but not always) evidenced by how long you spend there. (For further discussion of abandonment of U.S. residence, see Nolo's article, “How to Travel Outside the U.S. With a Green Card.”)
Given those legal restrictions, what happens if, even after fully intending to live in the U.S., your life circumstances change and you leave the U.S. for an extended time and then later wish to return? Perhaps your U.S. citizen spouse was transferred abroad for work, and you decided to basically go and take your chances that your green card would indeed be abandoned, and you spend at least one year outside of the U.S., but your spouse gets transferred back again. You want to come back, but are pretty sure you've lost the right to do so. What can you do?
This isn't as unusual a situation as you might imagine. Figuring out what to do next involves:
figuring out whether you really abandoned your residence in the first place, and
taking steps to get your residence back.
After a year or more spent outside the U.S., it should be pretty clear that you intended to abandon your U.S. residence – but there are exceptions.
Some green card holders, for example, take steps to avoid a determination of abandonment of residence by obtaining what's known as a reentry permit before their departure. (This is done by filing Form I-131, Application for Travel Document, with U.S. Citizenship and Immigration Services, or USCIS. See Nolo's article, “Reentry Permits: Preparing Green Card Holders for Long Absences from the U.S.” for details.) Reentry permits are good for up to two years at a time, and can be applied for more than once. Of course, we're assuming you didn't obtain one of these, but it's worth mentioning, just in case you did and forgot.
Or, the U.S. government could use its discretion to find that you didn't really mean to abandon your residence – which it is more likely to do in cases where unexpected circumstances arose that were beyond your control (such as a health problem or the death of a family member) during what was meant to be a short trip.
Again, we started with the supposition that your departure from the U.S. was due to something more straightforward and predictable, such as a job transfer. Nevertheless, if unexpected circumstances played a part in your long stay abroad, you might be able to apply for a returning resident visa (as described on the "Returning Resident Visas" page of the State Department’s website) or to go directly to a U.S. border or other point of entry and ask the Customs and Border Protection (CBP) officer to admit you as a returning resident, based on “good cause.” (You'd need to prepare USCIS Form I-193, Application for Waiver of Passport and/or Visa.)
Still, the above measures may not work, or you may not want to take your chances on flying all the way to the U.S. only to be turned away again.
Assuming the same family relationship exists through which you got your U.S. green card in the first place, your U.S. relative could start the process over from you, by filing an I-130 visa petition. By now, you're familiar with the rest of the process, all of which you would need to repeat.
Your application might raise questions with U.S. immigration authorities, however, who would find your old files, and wonder why you're applying for a green card when you already appear to have one. For that reason, some immigration lawyers recommend, just to make sure the record is clear, that you file Form I-407, Abandonment of Lawful Permanent Residence, before submitting the new I-130.
This is a sufficiently complex area of the law that your best bet would be to consult with an experienced immigration attorney, for help analyzing whether you did, in fact, abandon your U.S. residence and for strategizing what to do next.