The only drama I can think of with a sad ending is A Love to Kill, however, Rooftop Prince has a very bittersweet ending (I still cried). A Millionaire's First Love made me cry for about an hour after it ended, but I would highly recommend researching about the tradition of staining your fingernails at the end of summer before watching, as that is somewhat crucial to the storyline. Miracle in Cell no 7 is a really sad movie too. I mean it made satan cry...
By satan I do mean D.O. (basically all of EXO cried except Sehun who apparently has no heart).
My sister also said that the saddest movie she ever saw was called Hachiko. I'm not sure if it's got a sad ending, as I don't watch sad movies involving animals because I like my heart remaining sort of in one piece. I'm also not sure which language it's in because it's a Japanese movie, but she bought it in a store that only sells English speaking movies.