If you are a lawful permanent resident whose ten-year I-551 has expired or will expire within the next six months, you may renew your card by filing a Form I-90. If you are outside of the United States at the time of the card’s expiration, and you have not applied for the renewal card prior to your departure, you should contact the nearest American Consulate, USCIS office, or Port of Entry, before attempting to file Form I-90 for a renewal I-551 card. I would not leave the country with an expired card because it would create a problem for your return. I would certainly risk losing the money on the trip to maintain your green card, because once you leave the country you will be stuck waiting for the I-90 to go through before you can be readmitted. There is no grace period on the expiration of your card, so it would be considered expired.
The airline does not have to refund your trip, but you should contact them and see if you can reschedule based upon your immigration status problems.
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