We met Annie in episode 3x20, The Man Behind the Curtain when Ben first came to the island as a child. She was about his age and they became friends. She made wooden dolls, one of him and one of herself. She gave him the one of her and kept the one of him. The two became really close.
When Ben was older, with Richard's help he gassed the Dharma Initiative, killing them. He walked over to Horace and out of respect closed his eyes, but we never saw Annie, so we have to come up with our own answer as to what happened to her. Here are some possibilities:
- Annie and her family left the island before the purge, otherwise Ben would not have been able to gas the Dharma Initiative, or he would have at least gotten her out of there before he did.
- He's Ben, he let her die for what he considered to be the greater good.