Well, since technically it hasn't happened yet…
Setting that aside, in Norse myth Ragnarok will be the final battle which leads to the destruction of literally everyone and everything, so it would seem that dwarves and elves would get swept up in it, too.
However, I don't know if the actual myth states one way or another. According to Wikipedia (for what that's worth), the Voluspa, does mention both groups in passing.
Here's the relevant text (translated into English):
Yggdrasil shakes, and shiver on high
The ancient limbs, and the giant is loose;
To the head of Mim does Othin give heed,
But the kinsman of Surt shall slay him soon.
How fare the gods? how fare the elves?
All Jotunheim groans, the gods are at council;
Loud roar the dwarfs by the doors of stone,
The masters of the rocks: would you know yet more?
And that appears to be it. So they're clearly upset by it all, and presumably side with the gods?
So the answer is whatever you want it to be, really.
EDIT: TGerritsen beat me to it!
saves some broken figures from the lead pile.
