They are the negative emotions of Vanitas. I personally believe they can be created by anyone but only strong hearted people can give them physical form. I personally believe Terra's lingering sentiment is in fact an unversed created by his hatred for Xehanort, but in order to gain physical form it had to possess Terra's armor. Being created from Terra's hatred for Xehanort it exist simply to destroy Xehanort, but is an unstable existence and without Terra around to command it, it has stayed hidden at Keyblade Graveyard all these years.
I think Sora's Heartless in Re:Coded is in fact the remant or unversed of Sora's heartless that resided in the Journal as it was unable to take physical form. I think the XH in COM was in fact the remants of XH and it was a type of unversed as well that latched onto Riku, and just like XH it desired to take over Riku and gain a physical form.
I kind of think of Unversed as heart ghost in a way, remants of the heart that do not have any will or desire of their own but simply continue the desires or will of the emotions or memories of the people they originated from. Just like with a ghost, it is very rare and difficult for them to take on a physical form normally. Vanitas' pure dark heart however provided enough strength to make his unversed physical.
This is what I think their name means "Unversed" those not well versed in their own existence. They are simply remants or heart ghost of some form that do not have a will or desire and exist simply to continue their will of the person they were born from and they know nothing else or understand nothing else. Which goes into what Nomura said when he called them the opposite of human life, in that where as what makes us human is our unique wills and desires and personalities, and what drives us, where as unverse lack all of that and are simply exestentions of another being.
I may be drastically over thinking this but that is just my theorizing.
