I have a theory that Damon makes Elena to take the cure by forcing it down her. She is the attention of anyone who wants to become human again so vampires from around the world start to track her down.
Kai escapes from the other side and wants revenge on Damon and Elena. Not knowing Elena took the cure, he threatens Damon that if he doesn't get the cure, Elena dies.
Damon immediately regrets giving Elena the cure. When Kai finds out Damon hasn't got the cure, he kills Elena.