"Lumina: Looks like there’s one Yeul who wishes to be with someone other than Caius. Do you understand now? The power that shred the world apart, warped space and time, and pulled you into Valhalla, was the “invisible Chaos” – or simply, the many reincarnations of the eternally suffering priestess. It was all Yeul. It seems like the Chaos has calmed down a bit, but who knows when it will go crazy again. If I were you, I would hurry and find a way to save their souls, Lightning."
Can someone explain this line to me? lol.
As far as the invisible chaos is concerned... my theory is kind far fetched but...
All people have a piece of chaos in them. It gives them a certain amount of power in some cases, like magic. Yeul has always been an odd case, so it's likely her chaos is a bit different, she is the first human being and she is unable to be dissolved into the afterlife like other souls.
The same soul of Yeul is reincarnated, but is always a bit individualistic. So while the soul is the same, it could be that other facts are different, including them probably having their own piece of chaos. As all the Yeul's died, their chaos assimilated and because generally known as "invisible chaos." And since she died every fifteen years since the beginning of time, well, that's a lot of power that Etros is having to hold back. And it's the chaos of a person that has been suffering for all that time, and I've always held that chaos/power has been linked to emotions since the first game.
Lightning goes to save souls and take them to the new world but if she were to save Yeul's soul, she would have to take all that chaos with her, and it's too destructive to do that. So Yeul stays, but Caius refuses to leave her because even if it means destruction, Yeul is still a child and that person would be scared to be without her parent.
The Yeul's want to be with Caius with the exception of who Lumina points out.
If you read the novels, the many incarnations of Yeul never really got to live life, they were almost immediately taken away by Caius for her safekeeping. Most Yeul's seemed to take it okay, but one Yeul, the Yeul in AF500 (the last level of XIII-2), became bitter and asked Caius for the at least the last Yeul to be allowed to live freely. Caius agreed.
That Yuel was AF700 Yuel, or "Noel's Yuel." She was allowed to live and fall in love freely, and she fell in love with Noel but died young like the rest. So while every Yeul was focused on Caius, the last Yeul said that she wanted to say goodbye to Noel.
At the very end, he lets one Yeul go, and that's Noel's Yeul.