Claire was one of the central early mysteries whose story arc suddenly dropped to no relevance. The initial conflict between Ben and the Others and the 815ers centered around the Others inability to conceive children to term. Juliet was held on the island to solve the pregnancy issues that no child could be born on the island. The reason was never truly explained. When Claire arrived on the island pregnant, she was kidnapped by the Others, tested in the Swan station against an unknown infection. We would later learn that children had been born on the island before: Jacob and his brother, and Alex.
Everyone had an interest in Claire's baby except Claire herself. It was only after the relationship with Charlie did Claire feel comfortable with her child.
In season 5, Claire is living with Kate at the Barracks. When freighter mercenaries attack, Claire is blown up in her house. Sawyer digs through the debris and finds her, but she thinks he is dead Charlie. Following her rescue, Ben summons the smoke monster to attack Keamy's men. Claire is horrified by the monster's violence. She escapes into the jungle. Miles strangely stares at her during the march back to the beach. This is a clue that something is wrong.
During the night, she wakes up to find Aaron missing. She finds him in the arms of Christian. "Dad?" she says. When Sawyer asks where Claire went, Miles says she went off to the jungle. Sawyer only finds Aaron. When the crew rejoins Jack and Kate, they ask what happened to Claire since Sawyer is holding Aaron, Sawyer says "we lost her." This is when Kate assumes responsibility for Aaron and leaving the island.
Claire is next seen by Locke in Jacob's cabin. She is an apparent odd, drug like state. She has no concern for her child. She is with him (Christian, or the image of her father). After the O6 leave, Claire comes to Kate in a dream scolding her not to bring Aaron back to the island. Instead, Kate vows a personal quest to bring Claire back to Aaron.
For the three years of time gap in the O6 return, Claire has apparently been living the life of Danielle Rousseau. Living in the jungle, fearful of the Others at the Temple, hiding and setting traps. In one of the stark, gross and crazy props of the show, she is caring for a Dead Squirrel Baby as a substitute for her own child, which she was wrongly told by Flocke was being held by the Others at the Temple. It seems that during the three years in the jungle, Claire had continuous contact with "her friend," the image of Christian, which in reality was Flocke (MIB). Dogen said that she had become infected with "the darkness" and turned into a murderous, vengeful being.
When Claire is in the temple pit singing "Catch a Falling Star," Kate comes to apologize to her, and to rescue her. Claire is upset and angry at Kate. Then suddenly, the smoke monster attacks inside the Temple, nearly killing Kate.
If the sickness was code for being "put under a spell by MIB," then Claire's three years alone on the island only served his purpose of harassing the Others (Jacob's people). She was never a candidate, and she served no useful purpose except as self-pity baggage during the long meaningless jungle marches of Flocke.
For those who believe that Claire was killed in the freighter attack on the Barracks, then Claire's "disappearance" was no more than MIB creating another zombie killer as a tool on this island purgatory, just as he did with Sayid. Just like in her real life, Claire was discarded when something better came along (in Flocke's case, the weapon called Desmond who he'd throw down the Light cave). If Christian's words in The End were true, that her time on the island "was the most important thing in her life," then Claire's life was a miserable void.
So what happened when Claire disappeared into the Jungle with Christian? If she was alive, she replaced Danielle as the Island's crazy woman. She was an Other attacker and murderer. She became mentally unstable. She became a follower of MIB, who may have been the devil himself. For three years, she lived in the darkness; the pitch black evil of spiritual existence.