Padam Padam, but really this is a staple in MOST dramas so you should have a field day trying to find what you're looking for.
I personally hate seriously/terminally ill characters in my entertainment, esp when it's the lead! ::shudder::...
Scent of a woman - cancer
Snow queen - heart problem
90 days of love - warning its biological cousins in love
Autumn tale
A thousand day promise
Greatest love
My friend is still alive - one episode drama special
You should check out A Thousand Day's Promise. Uh it is so good that I even cried a bit, so if you want one an I'll character than I seriously recommend that one. Hope you enjoy it ????