I thought Libby/Elizabeth was working for Widmore I know I post somewhere else about this, I could be wrong. I don't remember seeing Desmond at Libby's funeral and I would think if Desmond had seen Libby he would of remembered meeting her I don't think his drunkerness would of cause that much of a memory lapse. Yeah I kind of like to see Desmond reaction knowing that the person he got his boat from that he crashed on the island had also crashed on the very same island. And I thought maybe the writers had to kill off Libby cause then it would be hard to explain her being there on the island because they had met off the island. I'm pretty sure that none had known or met anybody else on the island before the crash, I know there were near by's or passing another at one point or another before the island as we had seen in some of the flashback in first season.

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Standing in the ocean with the sun burning low in the west
Like a fire in the cavernous darkness at the heart of the beast
With my beliefs and possessions, stopped at the frontier in my chest
At the edge of my country, my back to the sea, looking east