Impossible Coin

The Impossible Coin is a coin in Tiny-Huge Island in Super Mario 64 that, as the name suggests, is not possible to collect. Along with this, the coin itself isn't seen in a "normal" game of Super Mario 64, as parameters in the game prevent it from spawning. The coin itself can be found potentially in any copy of Super Mario 64.

Analysis
In the code of Super Mario 64, there are parameters in the spawner object where the Impossible Coin resides in that make it impossible to collect. When the spawner object is loaded into a course, it spawns its five coins 300 units above it. It checks for walkable ground starting from 78 units above the coins and then moves said coins to the nearest floor triangle below them. When the closest ground floor triangle is above the coins' hitbox, they will unload from the game.

Since the Impossible Coin's hitbox is below the nearest ground triangle, the coin despawns from the course. This is the reason why the Impossible Coin cannot be collected at all by Mario.

Other "impossible" coins have seemed to be located in both Tiny-Huge Island and Snowman's Land. However, through physics exploits and glitches, these "impossible" coins are possible to collect. In a non-personalised copy of Super Mario 64, there's only one genuinely impossible coin.

Personalization
Like the Mystery Goomba, the personalisation A.I. of Super Mario 64 can allow the Impossible coin to be tangible. Since the Impossible Coin is in the object data of Tiny-Huge Island, the object spawner of it can be placed elsewhere through Dynamic Level Rearrangement. This means the coin itself could be collectible in some copies of Super Mario 64.

Along with the placement of the specific Impossible Coin, other coins can be unloaded due to Dynamic Level Rearrangement, which can allow said coins to be Impossible Coins. This can only happen if the coin hitbox is below the nearest ground triangle in their new placement.

Trivia

 * The term "Impossible Coin" was coined up by the Youtuber known as Pannenkoek2012, but was used beforehand for coins that were eventually found to be collectible. However, Pannenkoek did use the term for the coin that's impossible to collect, and he was the first to use the term for the said coin.