It is a stretch, but W Two Worlds has a small kidnapping theme. She enters the world of a comic book that her father writes and the hero of the story meets her and, instinctively knowing she is important to figuring out why his life is so strange (and tragic), won't let her leave till she tells him whats going on.. https://www.viki.com/videos/1105299v-w-episode-1?locale=en
Also This same guy Lee Jong Suk is in a chinese drama called Jade Lover I am waiting on that has hints of kidnapping in the trailer.
Thai Dramas:
Petch Tud Petch: Guy in a secret corrupt assassin ring thing escapes and is rescued by an undercover (police officer?) he suspects her and she suspects him..It's pretty fun :) http://www.dailymotion.com/video/x5vbdo7
Talay Fai: kidnapping midshow, it's worth the wait. http://www.dailymotion.com/video/x4fzojb
Rak Rai: love this show. Kidnapping towards end show around ep. 20 I believe. http://www.dailymotion.com/playlist/x52f8o
Roy Leh Sanae Rai: Kidnapping ep. 10 I Think. http://www.dailymotion.com/video/x2yjd3l