Upvote:4
As I understand it, if you have a paper I-94, you should give it to the airline when you check in for your flight to Korea. If they do not give you a paper I-94, and perhaps even if they do, your departure will be recorded when the airline passes your passport information to CBP.
But you won't "need" the form anywhere, and if you have one but forget to hand it to the airline, nothing much will happen. In this case, if your departure is for some reason not recorded, you can mail your I-94 and boarding passes to an address in Ohio to have your records updated.
You can check your I-94 database records at the CBP's I-94 site, and you can get more information about updating your records on their page I still have my I-94.
We also have several related questions on this site: