First, I know this may sound wierd and groundless, but if you think about it: We know that Claire's father is Christian Shapherd. Wich actually mean that Claire's real name is "Claire Shapherd". As we all know, Shapherd is marked on the lighthouse as possible Candidate, what if "Shapherd" may refer not just for Jack, maybe it refer for Claire as possible Candidate As well as Jack? Think about it: Why does claire is so important for MIB, if she is actually not a candidate?
So, what do you think? I know this is pretty much groundless theory, but it may be possible.