Foreign nationals who are green card holders are residents for income tax purposes unless they have never actually been physically present in the U.S. in that status.
Green card holders are resident aliens from their first day of physical presence in the U.S. in that status or earlier if they became resident aliens under the substantial presence test and have an earlier residency start date under that test. Green card holders remain resident aliens for tax purposes until they follow specified procedures for notification of abandonment of their green card status. These rules generally are not well-known among the foreign national community. (See IRS Publication 519 for information about these rules.)
Many (quite possibly most) green card holders who have departed the U.S. think that their green card status automatically expires with the end date on their Resident Alien Card (it does not) or that they are no longer subject to U.S. income tax obligations after they leave the U.S. Even though green card holders residing abroad might not be allowed to re-enter the U.S. on their unexpired green card by the U.S. Citizenship and Immigration Services because of an overly long absence, they nevertheless continue to be subject to U.S. income tax obligations.