Headscratchers: Lightning Returns: Final Fantasy XIII
So since time was destroyed in the previous game, nobody ages or dies, yet there is still a day and night cycle, people can still move, and things still happen. And Lightning can travel through the time that does not exist anymore. ...Huh?
Day and night are caused by a planet's rotation about its axis as it revolves around a star, and time has nothing to do with it. The Earth has rotated on its axis and revolved around the sun ever since it was formed, billions of years before there were any humans to record "time". "Time" is an abstract concept created, defined, and used only by mankind, and only after the human brain had developed enough to create and understand a concept such as "time." The Earth had a day and night cycle before we were around to measure time, and that cycle will continue even after we are extinct and not around to measure time. In the game, time was "destroyed" in the sense that the aging process has frozen, and so living organisms cannot die from old age. Just as the planet still rotates about its axis without "time," humans are still able to move without "time." As for Lightning, it has never been stated that she is able to travel through time in the game; rather, she turned to crystal in Valhalla at the end of XIII-2, and because Pulse became Valhalla, she remained in the world as crystal and awoke five centuries later, with a century being defined as one hundred years' worth of day and night cycles.
That really depends on how you view Time. Time can be considered a fourth dimension that touches the three dimensional world we live in- We can move up and down, side to side, forward and backward, essentially in an X,Y,Z grid. The fourth dimension comes into effect where we move from one point to another. At least that's one way to look at it, different scientists will tell you different things. Time has always been part of the universe before the Earth came into existence in this sense. So the idea that Time has been destroyed, but the concept of days and centuries is still around makes very little sense. Maybe it would be more accurate to say that Age has been destroyed.
The fact that it says centuries have passed is purely telling us how long it WOULD have passed if time hadn't been destroyed. It's also there to give us a frame of reference, so we don't get too confused. Or something similar to that.
Here's a better answer: Caius killed a goddess and shattered the space-time continuum. Of course time is going to do things that don't make sense, and there wouldn't be a story if people couldn't move.
Simple answer: What Caius did was stop birth, death and Entropy. Everything continues on just like it has, except nothing new comes into existence and nothing already there decays and/or leaves.
So Caius destroys Time itself. Lightning wakes up "five hundred years" later. By what measure of time?! This isn't a question of abstraction. The fact that Valhalla explicitly lacks linear time is the reason why Lightning and Caius can get away with so many temporal shenanigans in Final Fantasy XIII-2 (like Caius continuing to exist even after he is killed by Noel). Of course, it is possible that Caius' plans didn't have the exact result he intended...
Five hundred years relative to the individual. Valhalla may be timeless, and the aging process may have come to a halt, but Lightning, Hope, and the rest of humanity are still capable of perceiving the length of their existence as equivalent to five centuries.
Well, it might just be Lightning, considering the other characters don't seem to have changed much in five hundred years. Destroying time probably meant more than halting aging; perception of time would logically be altered, and everyone might be "stuck" in time in a sense. The five hundred years is probably a subjective measure of time, feeling roughly the same to Lightning/Lightning's prison as five hundred years would in a normal time-friendly universe, and meaningless to the world at large. This is of course based purely on pre-release material and conjectural logic.
They're saying it's five hundred years, even though Lightning's narration at the end of the previous game claimed this was after eternity. Don't ask me how "after eternity" makes any sense. Time is broken.
She said that in a way that it meant that from HER POINT OF VIEW, it seemed like an eternity. Its hard to judge how long you sleep for if you don't have something to tell you the time. She could've also meant it literally, as after eternity means after the end of time, and Caius destroyed Time. The point is, from the perspectives of the people living in Nova Crystalia, its been 500 years since the ending of XIII-2.