Have you checked your traps carefully?
I've had a case there I found a dead, rotten elk two tiles from my bear trap, and upon closer examination the bear trap was triggered but still standing (i.e. not collapsed). If that's happened to you, Sami would like to have a look at your save, because triggered tracks are supposed to collapse.
Apart from that, the only reason I know of of dead large animals is that they drown when the ice is too think. I occasionally find dead elks and reindeer on the ice beside a number of holes in the ice (and I've also used that as a hunting tactic). Smaller animals can also die that way.
It's not uncommon to have birds of prey take down birds, squirrels, and hares (and my characters have occasionally stolen their prey). Foxes, gluttons, etc. have been seen to kill and take small prey from traps, leaving only feathers behind (in the case of birds: nothing but an empty triggered trap is left when they took a hare or squirrel).
Hm, I think I once stole the kill of a wolf, although I don't remember what kind of prey it was.