[TOMT] Can someone help me find that one Old Romance Movie from 2000-2010 about terminal illness?

The premise of the story as far as I remember is that:

They started meeting as a child when the girl moved in to the neighborhood in her yellow raincoat. She is always sickly. They eventually got closer. But the girl often disappeared. This is how the movie was, full of timeskip as the girl constantly disappearing. She told the guy she is an alien. The story progress from childhood to adulthood. Then later on we learn she actually has terminal illness and she is going through therapy which is why she often disappear. The ending is that they were in this sort of open vast area, the guy bringing her there to show the sky as she passed away.

The most notable scene I remembered from the movie was when they were at the airport and there was a line. She told the guy not to cross that line.

Yea that is all I can remember. It was from a long long time ago, I can't even remember when I watched it. So my memory was hazy. Hope someone can help me find it!

Edit: Oh right, I forgot to mention. Its Korean film.