I think Clara is a normal human being from present day Earth who travels with the Doctor but then something happens and she gets cloned through time. Maybe the Tardis does it. The Clara in Asylum and The Snowmen were temporal clones. Since the Doctor is a time traveler, he met them first, leading him to go looking for the real Clara and taking her on as a companion which leads to her getting cloned through time. Thus the time loop is complete. Timey Whimey...
That's a plausible idea, given how fond Moffat is of causality-loop stories (such as "Blink" and the River Song arc) -- and how much he keeps returning to the same wells.