Believe me: it sucks big time.
So I thought i'd post some quick info in case anyone is wondering what to do in such case.
1) have some Korean co-worker call every possible place (airport, police station, the "national lost and found" office, your embassy, etc.)
2) Go to the nearest police station and get them to write a report. They'll probably say you don't need one but show them the embassy's checklist and they'll get their ass in gear
3) Get two passport pictures from any photographer. It would be worth to mention here that Korean passport photos are 5X5cm whereas the Canadian passport requires 5X7cm ones...
4) Download the application forms from the embassy's website
5) Get ready to pay something like 200$ for a round-trip flight to Seoul
6) Go to the embassy with all the documents and (reluctantly) give them the fee - 150$ Keep in mind that they're probably open only 2-3hours a DAY so don't go in the afternoon; they'll probably be chilling at the beach
7) Come back to Jeju with empty pockets and accept the fact that you won't be able to spend another dime for a few weeks because you were stupid enough to lose this precious document
8) 3 weeks later (or so), it SHOULD be mailed to you...
