It's called the Mystery Goomba, and for almost two decades no one knew it existed. In Super Mario 64, gamer pannenkoek2012 noticed that something was off: a Goomba was represented on the counter but not displayed in the level. Such set off a mission to find this Goomba, and in doing so he discovered that it can't be killed.
The saga started back in April, when the gamer first noticed the missing Goomba (only two of three were in visible). Through trial and error and a bit of cloning, pannenkoek2012 found that there was, indeed, a third Goomba, but no one could figure out where it was located (watch the video below to see the first part of this mission).
Not satisfied with merely knowing about the Goomba's existence, the gamer set out to find out where it was located and kill it. Surprisingly he was successful in locating the minion, but there was bad news to follow: it spawned at the bottom of the map for a single frame before disappearing.
Again, not satisfied with this answer, pannenkoek2012 set out to kill it. Several antics were tried, one that includes sacrificing Luigi for the greater good, but none of them were successful. As it turns out, the Goomba spawns below the point at which the characters die, making it untouchable.