From reading other people's theories and speculation, I come to believe that no one can die in Valhalla. It's a realm with no distinction between life and death. If someone dies he may disappear, etc, but due to the chaotic property of time, he is dead, yet not dead. It's quite hard to understand but from the secret ending, it can inferred that Caius knows that he is going to survive all along. Therefore, he doesn't hesitate letting himself killed, knowing that he MUST eventually exist, sitting on that throne. He saw that all possibilities in the timeline MUST result in his victory. Hence no matter what Serah and Noel do, he will in some way triumph. Well there is a small glimmer of hope apparently. But we don't know of that yet.
On a side note, do you notice that Mog doesn't have his clock staff during the ending CGI? It's actually mentioned in the fragments that Mog himself is just a dummy. The real Mog resides in the clock staff. So what if Mog is the last hope left? Has the staff been left in the void beyond, where chaos doesn't affect it? Look at Caius in the secret ending. He is supposedly in the void beyond, and he isn't affected by chaos. So Mog's real form might just be a very important plot device in the eventual continuation of the game.
Or... The developers may have actually forgotten to animate Mog's staff in the ending
On a side note, do you notice that Mog doesn't have his clock staff during the ending CGI? It's actually mentioned in the fragments that Mog himself is just a dummy. The real Mog resides in the clock staff. So what if Mog is the last hope left? Has the staff been left in the void beyond, where chaos doesn't affect it? Look at Caius in the secret ending. He is supposedly in the void beyond, and he isn't affected by chaos. So Mog's real form might just be a very important plot device in the eventual continuation of the game.
Or... The developers may have actually forgotten to animate Mog's staff in the ending