Paik Woo-Jung (Korean: 백우정) was the CEO of the South Korean corporation Paik Heavy Industries, as revealed in "D.O.C." Mr Paik was Sun's father and Jin's father-in-law, as well as Jin's employer. According to an overheard conversation in "D.O.C." as well as information from The Lost Experience, Mr Paik and Paik Heavy Industries had significant business dealings with the Hanso Foundation and the Widmore Corporation. Paik Heavy Industries seemed to be involved in various manufacturing industry sectors, including motor and vehicle manufacturing under the names Paik Motors and Paik Automotive.
As a child, Sun accidentally broke her father's glass ballerina. When he asked her about it, she denied that she had done it and blamed the maid. Mr Paik, after warning her that this would mean termination of the maid's job, chose to take his daughter's lie and subsequently fired the maid. ("The Glass Ballerina")
Mr Paik arranged for Sun to meet Jae Lee, the wealthy son of the owner of the Seoul Gateway Hotel and the hotel's General Manager. The arrangements were made through his wife Mrs. Paik because he thought it was time for Sun to be married. ("...And Found")
After meeting Sun and falling in love with her, Jin asked Mr Paik for permission to marry Sun. Upon observing Jin's sincerity, Mr Paik consented to their marriage. However, Mr Paik asked Jin to become an employee of Paik Heavy Industries as his personal "assistant" in return. ("House of the Rising Sun")("...In Translation")
After their marriage, Jin's mother attempted to blackmail Sun, demanding $100,000 in return for not revealing to the public that Jin's mother was a prostitute. Sun went to her father's office to ask him for the money she needed to pay her off, but Mr Paik was unwilling to give the money to her without knowing why it was needed. Sun told her father that she knew what he really did for a living, and always pretended otherwise, and would continue to do so if he gave her the money she needed.
When Mr Paik did not give in, Sun admitted she needed the money to spare embarrassment to someone she loved. Sensing that this 'someone' was Jin, Mr. Paik gave her the money, but warned her that, because the money was for Jin, the debt would be on Jin's head and he would work directly for Mr Paik, presumably in the line of work Sun knew her father did but pretended her father did not do. After a moment of hesitation, Sun took the money and left without saying a word. ("D.O.C.")
Later, Mr Paik found out about an affair between Sun and Jae Lee. However, instead of telling Jin about it, Mr Paik lied and told him that Jae was stealing from him, demanding that Jin kill Jae Lee to restore the family's honor. Jin, unwilling to kill, told him that he quit, but Paik laid his arm on Jin's shoulder and said that he was married to his daughter, so he was his son. Therefore, his honor was Jin's honor. Paik later confronted his daughter at Jae Lee's funeral, after he committed suicide, and said he wouldn't tell Jin about her affair because it was not his place, but she should return home to her husband. ("The Glass Ballerina")
After the rescue
Mr Paik and his wife greeted Sun at the military base where the Oceanic 6 were brought upon their return. Sun later confronted him, saying he was partly to blame for Jin's death, as he hated Jin, and they would not have been on the plane were it not for him. He began to admonish Sun for speaking to him in this manner but was shocked to learn that she used the money from her settlement with Oceanic Airlines to purchase a controlling interest in his company. ("There's No Place Like Home, Part 1") It is likely that he and Mrs Paik became the guardians of Ji-Yeon Kwon, Sun and Jin's daughter after Ajira Airways 316 was declared lost and the passengers, including Sun, dead.
Dr. Mittelwerk, in recent years, my honorable government has turned a blind eye to the questionable activities of your off-shore research station due to the lucrative business partnerships the Hanso Group has offered the proud people of this nation. Your joint venture with Paik Motors, for example, is a matter of great national pride, and we wish to continue doing that level of business with your firm.