The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at You Know, That Thing Where.
To Serve Man is probably the closest thing, but it seems to be restricted to aliens and monsters. Even with a very loose definition of "monster", an ordinary tiger is a bit of a stretch.
There is Panthera Awesome for dangerous wildcats in general, along the same vein as other things potentially dangerous to humans, such as Man-Eating Plant and just about anything in the Dire Beast index.
Also Just Desserts for when it's the villain who gets eaten by something, and Exit, Pursued by a Bear where they get killed or chased offscreen by an animal with being eaten often implied.
Edited by molokai198
Is there a trope for when animals eat humans in stories? Like how in the jungle book, shere khan eats humans even though its against the jungle law.