shards of Akatosh ... interesting
they come off godlike in a way if they are eternal , immortal etc
but yet they are killable , and the first dragon born "devours them "
so once the die where do there souls go other then being absorbed by a dragon born ....
maybe thats why during the first Skyrim trailer that voice say's " there's one they fear..... in their tongue he is known as Dovahkiin ... DRAGONBORN!"
however ive seen guards kill dragons in the game and the dragons corps just lays there .
blah blah blah blah now im babbling

Bad anology time!
Lets say those with a soul of a dragon: Dragons and Dragonborn, have a bit of rock in them that attracts that which is like itself, but cannot remove it from the body of a still "living" creature. In the case of dragons, their rocks stay on their corpse and can be hit with energy from a sufficiently powerful being with a rock, such as Alduin, and be resurrected. Dragonborn can permakill dragons because they have a rock and absorb the rock of the slain dragon, leaving nothing for one such as Alduin to resurrect. Mere mortals do not have a rock, so they cannot kill dragons as they have no means by which to absorb rocks, they do however have the ability to beat dragons into a corpsey state, because immortal doesn't mean invincible.