The White-eyed Chomp, commonly abbreviated to WEC, is an anomaly that changes the textures of the Chain Chomp to have their pupils absent, leaving empty white eyes. The anomaly never usually changes the behavior of the Chain Chomp itself, although it serves as an indicator to most players that their copy will undergo some level of personalization, whether it be notable or aggressive. Many players have encountered and documented their sightings of the White-eyed Chomp to varying validity.
The Chain Chomp itself behaves expectedly, attempting to attack the player until it's stump is ground-pounded, where it breaks the cage holding the star and hops off. However, what it signifies is what sets it apart from its 'normal' counterpart. The appearance of this anomaly often precedes major changes to the gameplay caused by the AI. These can range from almost all of the enemies in the game sharing its pupil-free complexion, subtle changes to the game's environments, or even larger ones such as the appearance of unexpected levels or the fourth floor.
The White-eyed Chomp can appear in other levels outside of Bob-omb Battlefield with a different behavior, however this occurrence is much rarer than the White-eyed Chomp appearing normally. So far it has been seen in Big Boo's Haunt, Snowman's Land or even the castle grounds. When it appears in these levels, it starts free and detached from its post. It will hop around aimlessly. If it spots the player however, it will give chase by lunging at them.
The White-eyed Chomp appears in both of jefftastic's copies of Super Mario 64, appearing and headlining in the first and seventh videos. In both of these videos, the White-eyed Chomp appears to act identically to the regular Chain Chomp and acts as a warning to jefftastic that further personalization is coming. Notably, the sign that warns the player of the Chain Chomp has its text changed in both videos. In WEC sighting it reads "Your fear is justified", and in Return of the White-eyed Chomp it reads ""you" already know this though".
The free behavior that the White-eyed Chomp can inherit could possibly be an unused behavior that the Chain Chomp was planned to enact upon being freed. In this scenario, the Personalization A.I. (which is already indicated by the White-eyed Chomp's appearance) pulls the unused behavior to be used on the Chain Chomp. Alternatively, it could be an altered version of the freed Chain Chomp behavior as seen in game, once again caused by the Personalization A.I..
This free behavior was replicated in Super Mario 64 DS on the Silver Star mission for Bob-omb Battlefield. A common theory is that most of the bizarre changes in the DS remake were caused by the developers basing the game of a highly personalized copy, and this could be another element erroneously carried on from that copy.