Their were worlds that believed in the three fold law. Somebodies, beings, were made of three.

If this is so and we already know that the heart becomes heartless, and the body becomes a nobody; what happens to the last part, the soul,what kind of being would exist devoid of a soul.

The three realms of Reality. Light, the realm of Beings. Darkness, the realm of those without hearts. The Inbetween, the realm of nothingness. The realms each have their own properties and laws, and they govern their own inhabitants how they see fit. There is something separating the realms, a barrier.
But...what if there were an upheavel? An unbalance in the power of light and dark?

The Separation is...fading away...the realms are melding, fusing together, now with nothing to hold them apart.

With the creation and destruction of Kingdom Hearts this balance has been lost, and a realm that has very little activity has become far more active in it's wish to set the balance right.

The realm of souls is the only way to balance the universe after such an upheaval. Though such a trigger to set off the realm of nothingness has not occured in a very long time.

Though the realm of souls is a neutralizing system it; because of the upheaval cares not for either side, light or darkness and is trying to once again create an uncorrupt balanced (utopian) universe.

The Princess, a Princess of Soul chooses in hope to help her people to bring back those other beings, the beings with no hearts. But bodies and souls.
The Princess ressurects the defeated Organization.
These beings she believes without knowing would help her save her people and stop the Hollows, for nobodies were of Twilight, just like the Twili.
They would know what to do.