So awhile ago I started watching this movie but I never finished it. I just recently started thinking about it and how I want to watch it and finish it, but now I don't remember the title. It's about this woman who was adopted as a child and goes back to South Korea to find her birth parents. She meets this guy who is sick (I don't know how, I just know he's sick) and I think they end up falling in love somehow. Like I said, I didn't finish the movie. It would be great if someone could help me out!

This sort of sounds like Rooftop Prince, though that's a drama not a movie. If you're sure it was a movie then I can't help. Maybe someone else knows.
I think it's the movie Maybe starring Jang Hyuk. 
was it Japanese, Korean?..
I found it! It does star Jang Hyuk, thank you!! ^^