We're sorry, but you wouldn't be allowed to carry that sort of thing over. The paraphysics of Caligo's world will most likely not hold the same laws as the world of Pandora Hearts, not to mention the negation of any supernatural effect on a character upon their arrival in Inaba. There is the possibility of having something drastic happen to Oz during his time in the TV World that may produce a similar slowly dying sort of situation, but that would be up to you.