Both the green card and passport must be current as trying to re-enter the United States with an expired passport or green card is likely to get a traveler into trouble. It could result in you being denied entry into the United States.
When you arrive at a port of entry a customs officer will examine your green card and other identity documents that you have with you. The other documents include a passport or foreign national I.D. card. The officer will determine whether you are eligible to enter the United States. Traveling outside the United States for less than six months does not present any problems to green card holders as long as you have the green card with you upon your return. If you lose your green card whilst traveling abroad, you can get a transportation letter from the nearest U.S. embassy or consulate.
When a permanent resident has been out of the United States for a length of time longer than a year and less than a total of two years, a re-entry permit is required in order to re-enter the country. This re-entry permit is required in addition to a valid green card. Re-entry permits (Form I-131) must be acquired in the United States before a permanent resident embarks on her journey. The application may be approved only if the application is submitted while the person is in the United States. Applications require fingerprints and photographs in order for it to be considered. If the applicant leaves the United States while a decision has not yet been made on an application for the re-entry permit, it is unlikely that this will affect the outcome of the decision. However, if they have left without having their fingerprints and additional biometrics collected, it is possible that the application will be denied. It is unwise to travel in such a situation as the application could be denied while the permanent resident is out of the country and in that case the traveler may be refused entry into the country.