As the anagram with her name which when you re-arrange Xion you get "No I" meaning she doesn't have a somebody like the rest of the Organization members. However, I repeat to anyone who thinks she's a nobody of Sora or Kairi she's not. Xion's name does not fit the naming scheme of the other Organization members, as it should be an anagram of "Kairi" and "X" if she was Kairi's Nobody. However, her name could in fact follow the naming scheme which Xehanort's does - If the "X" is removed, his name is an anagram of "No Heart" and "Another". Xion's name easily fits this pattern - for her, the anagram would be "No I", possibly implying that unlike the other Organization members, she doesn't have a somebody. This would also play into the reason why the Organization remains "Organization XIII", even with her in its ranks.
Possibly, Sora's "leaked" memories fused with Xion after the Castle Oblivion incident, explaining Naminé's question as to whether or not Xion could endure it, maybe meaning if Xion could endure giving the memory back to Sora, which could lead to her tragic fate. Whatever the case, she could be encasing some of Sora's memories, causing her to have a similar existence of a Heartless with the characteristics of a Nobody.