Toad's Tool 64 Star

The Toad's Tool 64 Star refers to a group of anomalous objects in the penguin slide segment of Cool, Cool Mountain in Super Mario 64 that can only be viewed in the emulator known as Toad's Tool 64 with a process known as "Extend Level Boundaries". These objects include coins, a 3-Star Castle Door, a butterfly, a jumping fireball, an open cannon, Spindrifts, a static 3D object, another penguin NPC, and of course, a Power Star.

This Power Star was the main focused object out of any other in the odd set in Cool, Cool Mountain, and obtaining it was something people wanted to do. It was alleged to be the 121st Star in Super Mario 64 by these said people too. However, obtaining the Power Star is impossible, even when using Toad's Tool 64.

Theories
What is unique regarding the anomalous objects would be that they are only visible in one emulator and one emulator only; Toad's Tool 64. Since every copy of Super Mario 64 is personalized, this can mean that this personalized copy of Super Mario 64 had added in these objects into the game. It is possible that the emulated copy malformed in some way, causing data to be added when there shouldn't have been, since adding objects isn't possible through Dynamic Level Rearrangement. However, that seems to be based on information given that doesn't scratch the surface of the personalization AI.

This unique copy of Super Mario 64 could also be personalized in a way that adds the objects in. However, viewing the objects in said copy's emulator turns them all into Snowman heads. Along with that, these objects don't load in the base game. This could mean that before the copy was emulated, the game was in the middle of processing objects for the player's personalization, which could probably explain the unfinished quality of these objects.

That all is implying that the build that the emulator runs is the final build of Super Mario 64. It is possible that this build that the emulator runs was a slightly earlier build of Mario 64, with the leftover objects in place. This copy of Mario 64 could have been leaked somewhere beforehand, and was used for this emulator.