His Horcruxes tied his main soul to life.
When the Dark Lord’s Killing Curse rebounded on him, it both ripped his soul from his body as his body was killed and fractured a piece off of his main soul, which went on to live in Harry.
“Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself on to the only living soul left in that collapsing building.”
- Harry Potter and the Deathly Hallows, Chapter 33 (The Prince’s Tale)
When the Killing Curse rebounded, his Horcruxes worked as they were meant to - they tied his main soul to life by keeping part of his soul outside his body, ensuring it couldn’t die even if his body was killed.
“Well, you split your soul, you see,’ said Slughorn, ‘and hide part of it in an object outside the body. Then, even if one’s body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged. But, of course, existence in such a form …”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
When his soul split, both pieces were tied to life, as up until the moment of the split, they were both part of the main soul that the Horcruxes tied to life. The piece that fractured off was still part of the main soul until it had split, so it was also tied to life by the Horcruxes then. It of course lost that protection after it was no longer a part of the main soul, but it was a part of it at the time it split, allowing it to live and attach to Harry.