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ability

Ellone is able to experience the past of people she has met through others. She sent Squall and the others to Laguna's past hoping they could change the way things turned out. But that's impossible. Laguna just thought that the fairies had come, but Ellone didn't realize how much she was loved until seeing things through Squall.

Ultimecia wants Ellone's ability to achieve time compression. The thing is, in tc (time compression) no one can survive long. Except Ultimecia herself. When she is the only survivor, she will get enormous powers comparable to those of Hyne, the creator of mankind and first sorceress.

This confuse you enough? Go here for a longer and more detailed explanation.

reason

When Raine died, she was calling out for Laguna, the father of her son. Ellone thought it was so wrong that he couldn't be with Raine then. That's why she kept on going to the past with Squall & Co. To try to tell Laguna to be at Raine's side. She thought she could change the past somehow, but realized she can't.

Though through these little insights on Laguna's mind, she realized how much she was loved and that Laguna really wanted to be by Raine's side, but couldn't because of his duties as the president.

Of course, in the escape capsule she goes to Rinoa's past because Squall asked her. It is then that she reveals the reason behind her earlier visits.