Disclaimer: I do not own kingdom hearts; just this theory!
I can fully explain what Nobodies are, and how they're formed. Which makes me question Vexen's intelligence since I'm only in my first year of high school.....But anyway!
So to understand what a Nobody really is, you have to go back to their formation.
It says that they lose their hearts, but look at it rationally. The heart is an organ in the human body for pumping blood. It does not just up and think 'Hey, I like the dark side! I think I'll go walk out my own mouth!' No. That just doesn't happen. So I figure that it would be the soul, since the two are often confused. Besides the soul is not a physical aspect of a being and is also what is said to hold ones personality and who they are. This would explain how anti-Sora became Sora again.
So when a person turns themselves over to the darkness, their tainted soul is forced out and the darkness allows it to physically manifest itself in the form of a heartless. The body that's left behind either flies off to become a dusk, or in the case of a Nobody, dies.
Darkness is an element; hence it is in constant motion. So the body of a Nobody dies- momentarily. Because the same darkness that created the heartless is still flowing through the body, restarting all the organs necessary for life to create another henchman. The circulatory system however, is no longer needed since the darkness has taken the place of the blood. Emotions are also dubbed by the darkness as an unnecessary hindrance, so the glands in the brain that make the chemicals that stimulate emotion are also left dormant. This does not mean these organs are not present, just not needed.
The brain is restarted so the darkness follows the instructions of the instinctual mind. But since the brain has been restarted, and learning is essential to understanding and power, and remembering is essential to learning, the memory function stays intact.
Gradually, over time, a consciousness forms within that mind, and slowly IT begins to control the darkness, instead of the other way around. The reason that the Nobodies think that they are their Somebodies is because they have their memories. However, since they have been out and living, and learning from the time of their creation, they know more then before, making them a completely different being. Having the same chemical make up as their Somebodies plays only a 50% part of who they ARE. "People are only half of who they are born as, the rest is experiences." Take Sasuke from Naruto as an example. He's a clinically insane, depressed child. But what if he still had his family? Yes, he would still be a bit broody, since that is his nature, but he wouldn't have 'gone off the deep end' would he? That's how experiences can effect people.
Now knowing all of this, it's simple for a Nobody to become a full person again...in theory. All it would take is an extremely emotional situation to stimulate the chemicals into snapping through the nervous system, which would restart the heart, sending blood though the veins and arteries, flushing out the darkness. The difficult part is stimulating the emotions, since everyone reacts to things differently. It would take time, but I think it would be possible!
I hope this sounds ok....It feels like a research paper to me...But I'm really proud of this theory!