In fact, just about any mutant will gladly drag your battered corpse back home for supper.

Bloodsuckers are also wont to do this.

If you're killed by a Tank Commander, it will walk over and punch your dead corpse.

According to the authors, the ogre enemies were supposed to pee and laugh after killing the player, but that never got introduced due to 'time issues'.

Killing Floor actually has an achievement based around killing specimens that are feeding on your dead teammates' corpses.

Jurassic Park: Trespasser also has the 'eat your corpse' variety of animations.

Besides that it's possible to have them shoot their own corpse.

If a player is taken as a meatshield, they will usually have the respawn time countdown as soon as they are picked up.

The No-Holds-Barred Beatdown execution (or Beat Them With Their Own Arm if you're Locust) could be this since the player is already dead as soon as someone does it. CTL (Capture the Flag, but a player is the flag) has this when someone caught the leader since the game lets you snap their neck after the round is won. In TDM if someone got killed and their body's still there, someone, usually the killer, will shotgun the body into tiny gibs.

Gears of War 3 has a somewhat steady example when it comes to multiplayer.

Gears of War: Done with weapon-specific, instant-kill executions.

The third game, Ice Age, takes it Up to Eleven where now everything that isn't a pig or an archaeopteryx can kill you: most of the animals thrash you around instead of actually eating you (most of them are herbivores, but the carnivores do this too) but the brontoteriy jumps up and down on you and the diatryma really does eat you. Most of the dinosaurs use the same basic animation of knocking you over and eating you while you're on the ground, but some have unique animations, specifically the T-Rex, which picks you up in its mouth and thrashes you around.

Carnivores: When you die, you're treated to a lovely scene of the dinosaur eating your corpse.

Someone is already looting that corpse