The Fail Whale (Defectus cetaceans) is a tamable monster that has totally stopped trying to be a whale anymore.
Pets of Godville
No good at being a whale at all|
|Tame at levels
It no longer knows how to swim, and has become completely dependent on birds to move from place to place, which they do in exchange for the whale's mercy on young birds (otherwise treated as attack targets) when they land on the water to eat zooplankton.