Hearts don't usually gather to form Kingdom Hearts
but they did for some reason in KH2, probably because
of the Organization's interference.
The fate of hearts and soul in natural death is
still a mystery but personally I don't think it has
anything to do with the Unbirths, though I do
consider it as a possibility.
Here's my thoughts on the Unbirths: When Nomura was first asked about the new enemy, he reminded the fans that the main Heartless was called a Shadow and the main Nobody was called a Dusk. Based off the dirrections of the Crossroads, there are Light, Dawn, Darkness, and Nightfall. Possibly each enemy might be part of a different domain. Shadows are of Darkness of course because they are 'darkness made real'. Nobodies, though they claim to be of nothingness, are twilight beings who exist inbetween, and like nightfall they are destined to fade into darkness. I think Unbirths are comparable to that of beings of the Dawn domain, since dawn is essentially the birth of the day.
More specifically, I think MX will interfer with world order and Kingdom Hearts in BBS and by affect Unbirths may spawn directly from Kingdom Hearts itself, which would do well to explain how they come into existence without the 'lost of heart' process that produces Heartless and Nobody. I think Unbirths will be composed of hearts that have yet to be born into the world, which further explains their name. I think the concept of the birth of the heart has yet to be properly explored in the series so it seems fitting that such a concept should be explored in Birth By Sleep.
I think at the end of BBS the knights will be at least partially successful in stopping MX and by doing so will correct the damage to world thus stopping Unbirths to exist. (Perhaps though something else might harm world order which is why Heartless and Nobodies come into existence soon afterwards)