In Season 4’s finale, Sun approaches Charles Widmore and tells him that he knows that more than the Oceanic Six got off the Island and then tells him to call her. Widmore asks her why she’d want to help him, but she doesn’t answer.
I think the answer is obvious.
John Locke has apparently left the Island under the pseudonymn Jeremy Bentham. Also in Season 4’s finale, Ben Linus kills Charles Widmore’s mad dog mercenary-for-hire, Martin Keamy, even though Keamy had warned him [and Locke] that he’s been wired with a “dead man’s trigger” which will detonate the freighter Kahana if he dies. Ben kills Keamy anyway, begging off later that it was a crime of passion [Keamy was goading him, reminding Ben that he’d killed Linus’ daughter in cold b lood] and a crapload of C4 aboard the Kahana explodes. Sun’s husband, Jinn, was still aboard the freighter when it exploded. She watched the event from a helicopter above.
Jeremy Bentham [aka Locke] has probably told Sun that Ben killed Keamy even after the latter warned him about the dead man’s trigger. She blames Ben for Jinn’s death, since the freighter disaster could have been averted. I doubt she buys Ben’s crime of passion excuse. [I’m not sure I do either.]
She wants revenge. That’s why she’s willing to work with Charles Widmore.
–Sirius Knott
Defending Genesis 
Sun said she blames 2 people for Jinn’s death. I believe that she blames Jack for stopping Kate when she went to go get Jinn. My proof is after she told Kate she doesn’t blame her for Jinn’s death she asked her “So hows Jack doing?”