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Jack has already found out after he gave the eulogy at his Father's funeral (when they got off the island). Claire's mother told him they we're related (half brother/sister) but believed they had never met as she "died" in the crash.

Claire has been missing for some time now having walked off into the forest on the island one day. Its anyone's guess if she will re-appear. Presumably Jack will tell her if they ever meet up again.