The following extract was taken from an Interview with Yunjin Kim.
"Last season, Kim’s character, Sun, learned she’s pregnant. Given her initial reluctance to inform her husband, Jin, of the pregnancy and considering that a doctor previously diagnosed him as being sterile, Kim says Jin may not be the father of the child. “As soon as I got the script, I called [executive producer] Carlton Cuse and said, ‘I need to know so I can act.’ He said, ‘I think it’s good that you don’t know. Do several different types of takes - some where you actually know for sure, some where you’re very ambiguous about it and some where you’re completely sure he’s not the father of the baby.’ So we did several takes, and the one that they used was the most ambiguous one. I think they want to leave it open for a reason, and it’s driving me crazy that they’re not even going to tell me about it.”
The show’s ambiguities allow fans to form countless theories about what’s really happening on the island. “Whatever theory you have, it kind of works,” Kim says. “You could apply yourself to any character, any situation, and any theories you have kind of make sense.”
As far as Sun’s pregnancy is concerned, Kim speculates that Michael, who Sun had a notable attraction to in the first season, may have fathered the baby. “That’s another possibility that I think the producers are thinking about,” she divulges. “It could be his baby. [It would really change the balance of things on the island], especially since he just left the island.”
Source: The Trades