This question struck me when I read: Why didn't the piece of Voldemort’s soul in Harry come back to life with Harry? It is not a duplicate. What concerns me is which soul is the one in King's Cross and why did or didn't it get back (depending on which part of Voldemort it is)?
The answers there say that it was Voldemort's main soul that was in the station but that is different from the answer I got here.
The “King’s Cross” that Harry ended up in was the place between life and death. The piece of the Dark Lord’s soul that was in Harry was simply killed, so it didn’t go there. That piece wasn’t between life and death, it was just dead. It didn’t get a chance to choose to live. Dumbledore explains to Harry that it’s gone.
“So the part of his soul that was in me …’
Dumbledore nodded still more enthusiastically, urging Harry onwards, a broad smile of encouragement on his face.
‘… has it gone?’
‘Oh, yes!’ said Dumbledore. ‘Yes, he destroyed it. Your soul is whole, and completely your own, Harry.”
- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
Their conversation continues directly after that quote with Harry asking Dumbledore, if the bit of soul in him is gone, what the creature is. Dumbledore says it’s “something beyond help”, but the implication is that it’s not the piece of soul that had been in Harry.
“But then …’
Harry glanced over his shoulder, to where the small, maimed creature trembled under the chair.
‘What is that, Professor?’
‘Something that is beyond either of our help,’ said Dumbledore.”
- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
This also explains why there’s only one mutilated baby creature, instead of one for each Horcrux. If all the destroyed pieces of soul ended up there, then there should be more of them - except for Nagini, the other Horcruxes were all destroyed by then. If each piece of soul that was killed (since Dumbledore confirmed that the one in Harry was indeed killed) went to King’s Cross, then there should be more of them. Even if it was only recently killed bits of soul that would be there, the diadem was destroyed shortly before the battle.
However, there was just one piece of soul in that place between life and death - the Dark Lord’s main soul, which did indeed return to life from King’s Cross as Harry did. He may have had the choice to die, like Harry did, but ultimately he did come back to life from there.
J.K. Rowling addresses this in the F.A.Q. of her old website - she confirmed that indeed, that creature is the main part of the Dark Lord’s soul.
What exactly was the mutilated baby-like creature Harry saw at King's Cross in chapter 35 of 'Hallows'?
I’ve been asked this a LOT. It is the last piece of soul Voldemort possesses. When Voldemort attacks Harry, they both fall temporarily unconscious, and both their souls - Harry's undamaged and healthy, Voldemort’s stunted and maimed - appear in the limbo where Harry meets Dumbledore.
- F.A.Q. on J.K. Rowling’s website
Both evidence in the book itself and J.K Rowling’s statement indicate it’s the main part of the Dark Lord’s soul.
As for why the Dark Lord’s main soul survived, when he was hit, he still had one Horcrux, Nagini. As long as he had at least one Horcrux, he was still tied to life. In addition, he had Lily’s blood protection on Harry in his blood, which may have factored in as well (though it may have only been able to heal him if he chose to show remorse, and not worked to tie him to life by itself).
“He took your blood believing it would strengthen him. He took into his body a tiny part of the enchantment your mother laid upon you when she died for you. His body keeps her sacrifice alive, and while that enchantment survives, so do you and so does Voldemort’s one last hope for himself.” - Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
Even without the blood protection, though, he couldn’t truly die with a Horcrux still remaining, and Nagini was only killed after he’d already regained consciousness.
Whe Voldemort first tried to kill Harry when he was a baby, a sliver of Voldemort's soul attached on to Harry himself. When Voldemort uses the Killing Curse in the forest, he uses the Elder Wand to do it. Harry was the master of the Elder Wand at that time. So, the Elder Wand would not harm the soul of its master. But it could harm the bit of Voldemort's soul inside Harry. Lily's blood protection was also a major reason. That is why it was Voldemort's soul was found in the station between life and death.
It had the form of a small, naked child, curled on the ground, its skin raw and rough, flayed-looking, and it lay shuddering under a seat where it had been left, unwanted, stuffed out of sight, struggling for breath.
-Harry Potter and the Deathly Hallows
However, it was not Voldemort's "main soul" as described in the question. It was a piece of Voldemort's soul that was lodged in Harry.
