Alyssa

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When Noel and Serah step into the gate in Academia... and she gives the most evil grin everrrr! What is up with that? I was OMG-ing at the screen the entire time, especially when the gate did malfunction and seperate the two. Who da fudge is she??

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What ever her motivations were, she was a villain of sorts. Despite that, though, when you step into the gate in Academia 4XX, the last line she says in the game is "I'm sorry, but you're building a future where I don't exist. Good bye."

And then, when you return, if you go looking for her she isn't around. Additionally, if you talk to some NPC's, you find that some of them are confused. One in particular says, "Wasn't there a woman who was always with the director? What was her name?"

Alyssa herself ended up being a paradox. Perhaps something Serah and Noel did make it so that she actually did die during the Purge, rather than her friend. How this might have occurred is unknown; but, after all, when you change the future you change the past.

But, again, her motivations to working with Caius are a mystery. We never even see them together, it's only implied.

EDIT: The Final Fantasy wiki says that she was revived by Etro as well and that she was actually having dreams of what her fate should have been:

"As they all go their separate ways, Alyssa stops and looks back in Noel, Mog and Serah's direction, smirking with a grim expression, though Mog is the only one who notices. It would be later revealed that Alyssa obtained the Artefact from Caius upon realizing that the actions of Serah and Noel restoring the timeline would result with her ceasing to exist. She later apologize to them for her betrayal, saying that she cannot exist in the future they are trying to achieve, and says goodbye."

So, she regretted her actions, and died as a consequence.