From Bulbapedia, the community-driven Pokémon encyclopedia.
Pokémon Yellow is a special edition of the Generation I games. It introduced the friendship system, which was improved and completed in Pokémon Gold and Silver and has since become a staple of the main series. It also added other features, such as walking Pokémon, which are exclusive to Pokémon Yellow and Pokémon HeartGold and SoulSilver, and the Pikachu's Beach minigame. Some aspects of the game's initial design did not make it to the final release, either due to time constraints or due to its heavy reliance and basis on Pokémon Red, Green, and Blue.
Data exists for a battle situation when the Trainer has no Pokémon, though it isn't actually used when entering a battle with no Pokémon in the final release. In this case, selecting any option other than
RUN shows the message
Hurry, get away! This may have been a prototype for the initial battle with the wild Pikachu at the start of the player's adventure, as the player has no Pokémon at that point. It could also have been planned for a possible battle against a wild Spearow with Pikachu unable to battle, making it closer to the events of the anime.
This unused element can be seen better on the linked YouTube video.
An unused music theme has been encountered in the internal data. (link) It is not known where it would be used but it is possible that it relates to the aforementioned "no Pokémon" battle system. However, it is not stored in either the battle, overworld or cave soundbanks. It is located in the minigame and "special Trainer" (Jessie and James) soundbanks, where the Pikachu's Beach music is stored, which is partly why this track only exists in Pokémon Yellow.
It may be worth noting that it closely resembles the battle music theme with Madake from BUSHI Seiryūden: Futari no Yūsha (link) for the Super Famicom, a game that Game Freak developed and released in January 1997 after the release of Pokémon Red and Green but before the Japanese release of Pokémon Yellow.
There is unused radness data for a score of 750 points in the Pikachu's Beach minigame. It is impossible to achieve this score regardless of how many flips Pikachu does or how they were performed.