Is there any dramas where the ML broken(beause of something happened to him at past it can be anything revenge, ill or sad past life ) and made him to look like monster? 

And beause of a thing happened to him at past he is cold to everyone...

No one can fix him until he meets FL and she helps him to get back in his real life.

Idk why but I like this kind of drama

Please don't recommend me dramas where FL or ML chase after second lead(I hate this so much in dramas specially when they reject main role beause of it)

Ex: Kill me heal me (love it so much)  , moon lovers (I drop it beause of tragdy ending and Triangle love) , Blade man (haven't try it yet) , Hong Gil dong (2008) 

Madame Antoine

and to lesser degree:

and if you're interested in a trope "playboy is not interested in love or commitment until he meets.." you can watch The Great Seducer

The ML is genuinely viewed as a monster:

  • Gu Family Book - the ML is half gumiho and at one point his is also a suspect in the wake of several murders (warning: the ML does start out liking the SFL and doesn't really notice or fall for the FL, who is dressed as a boy, in the beginning)
  • Falling for Innocence - the description describes the ML as "a cold-blooded corporate raider... a cynical, self-defensive, suspicious sociopath"; that pretty much covers it
  • Hello Monster - the ML is a bit arrogant and is a somewhat cold / logical person; events in his childhood lead certain people around him to view him as a monster and he grows up questioning his own nature

The ML is broken and rude / cold / strange / or isolated, but not really viewed as a monster: 

  • You Who Came from the Stars - the ML is a basically-immortal alien; because of his identity / need to hide his immortality and the fact that he can't eat with humans without risking his health, he is quite isolated and reclusive; on the rare occasions that people discover his powers, they sometimes view him with fear
  • Just Between Lovers - after a tragic accident and rough upbringing, the ML has lots of anger / survivor's guilt / self-hate
  • Thirty But Seventeen - after a tragic accident, the ML's self-blame and guilt leads him to isolate himself; he's viewed as strange and difficult to deal with
  • Healer - the ML is an orphan who is isolated from society; his home / hideout is in an abandoned construction project and his only friend is a middle aged female hacker who is his business partner; he uses the codename Healer for his work as a man-for-hire; he is an excellent fighter but not a malicious person, just isolated and not interested in interacting with society; his goal is to buy and move to an uninhabited tropical island
  • School 2017 - after a tragic accident, the ML feels guilty, angry and suffocated; he isolates himself and acts rude or indifferent; he's viewed as arrogant, aloof, and entitled
  • Sungkyunkwan Scandal - the ML's rigid and righteous nature and unwavering commitment to his principles make him difficult to get along with (he really can be a stick in the mud); the FL is the first friend he's ever had
  • Marriage Contract - mostly because of his family dynamics, the ML is cold-hearted, rude, demanding and arrogant
  • What's Wrong With Secretary Kim - after a tragic and traumatizing incident, the ML copes by developing a self-obsessed personality and huge ego that makes him difficult to deal with; he also has panic attacks or reacts strongly when he encounters certain triggers related to the traumatic event
  • Come and Hug Me - the ML isolates himself as a child and is isolated by society as an adult because of his connection to a serial murderer; he is never mean or unnecessarily rude (in fact he's generally excessively polite), but he is quite reserved, lonely, and isolated
  • My ID is Gangnam Beauty - the ML is extremely good looking and often hounded by admirers, and his father is a fake and image-obsessed congressman; as a child he also sees things that lead him to believe that his mother abandoned their family to have an affair with a younger man; as a result, he hates superficial, looks-obsessed people; he tends to isolate himself and often comes across as cold and is sometimes perceived as arrogant