They would get bought out. Everything gets transferred...all of the securities on the loans and shit except the buyer gets them at rock bottom prices. But, IF they were to completely failed it is not an investment bank so they are FDIC backed up to $100,000 - $150,000 per person....although this doesn't really apply to you oweing them. However, there is no circumstance where you wouldn't have to pay even if Citi disappeared.