Yeah, since you asked.
Prior to leaving for the trip, I called the Embassy in Atlanta and they assured me we woudln't have a problem.
When we got to the airport and were ready to board Asiana they called immigration in Korea. The immigration officer there wouldn't accept the extension letter so long as the expiration date on the actual green card was expired. So, we were denied boarding. Asiana showed us as "abandoning the flight", so we couldn't even get a refund.
(I've since contacted the embassy again about this matter, and they said the ROK immigration officer was wrong, not that it's any recourse).
All wasn't lost. We spent an extra three days in Thailand and had a great time. But, I had to buy a new ticket home. Due to the last minute booking, it cost me an extra $2400 which wasn't expected for our trip. Making matters worse, it was a long flight. Bangkok - Abu Dhabi - Dublin, Ireland and then back to Florida. (Qatar seats were REALLY uncomfortable). Air Lingus was much better, but it's the first airline that I can recall that charges you for everything on International.
That said: When we got to Dublin we learned that the airport doesn't have a "transit" area so we also had to clear immigration. Wife didn't have an EU visa. We explained it, and the immigration officer was REALLY nice. He granted her a 24 hour Visa rather than being deported. (So we got to see Ireland for a few hours during our 10 hour layover).
All of this could have been avoided if the USA would have just issued a new card with a current expiration date.
We are actually applying for her to get a tourist Visa for Korea now so she can go and visit. (Technically she shouldn't need one, but this time not taking a chance).