I have a lost theory. I think that Jack’s dad is some sort of ghost. I think Claire went with him because somehow she died and he was helping her to the other side. Remember she was saying that she was dizzy after the house explosion. Maybe she was more seriously hurt, and died in her sleep.
Anyway, it’s my theory.
I think you’re right. I noticed that when Sawyer found her, she was covered by a sheet. At the time I thought that was kind of goofy, given the fact that the rest of the house was blown to smithereens. Also, Miles the Ghostbuster was just a little too interested in here. I think she’s dead.