I'm not perfectly sure what you're asking, but I think you're asking about how Sun "knew" Jin was dead?
Sun assumed Jin died because she saw the boat that she knew he was on explode while he was on it. Fairly reasonably, she assumed that when she saw that explosion that it took him with it. She didn't need Locke or Ben or someone else to go and tell her. I'm pretty sure if I saw a boat blow up I'd assume the people on it didn't make it, too, but who knows.
Now, a question that I'd like answered about Sun is that Ben promises to bring her to someone who can prove that Jin is still alive. As far as I remember, Mrs. Hawking never says a thing about Jin, to say nothing for proving that he's still alive. What do you think it was that convinced her to get on the plane?
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