Origin: Sun did not know Widmore until she left the Island, though coincidentally, she once used a pregnancy test that was made by Widmore Labs
Since Then: Though Jin supposedly died on Widmore's ship, Sun blamed Ben for his "death", and she sought out Widmore's help because they shared a common enemy. She first approached him openly on the street, and this audacity shocked the man. Widmore later had her held at London's Heathrow airport, where the two conspired to kill Ben. Once Sun reached Los Angeles, Widmore posted her several surveillance photos of Ben - and a gun.
Sun didn't end up killing Ben when she found out Jin was alive, and she instead traveled with him to the Island in 2007. Widmore ended up coming to the Island as well via a submarine, and he retrieved Sun's camera from her crashed plane. He later imprisoned Sun along with Jin and several followers of the Man in Black in cages, therefore, he was ignoring their earlier off-island partnership. Widmore was later killed by Ben at the Barracks while Sun died with her husband Jin on Widmore's submarine.