Right now I know that non-legendaries disappear forever in Emerald and Platinum, and legendaries in Emerald (not sure about Platinum) reappear when the player leave and re-enters the location. I heard that they all disappear forever in some games, or they reappear when the player defeats the champion. Please don't question my curiosity.
In Generation I and II games, in most instances, if the player runs from any of these Pokémon, it becomes permanently unavailable. However, in Pokémon Gold and Silver, the Electrode in Team Rocket HQ will remain even if run from. Starting in Generation III, if the player runs from a Legendary Pokémon, the Pokémon reappears when the player leaves and re-enters its location, but other Pokémon still become permanently unavailable. Starting in Pokémon Platinum, if the player defeats or runs from an in-game event Pokémon, then it reappears next time the player enters the Hall of Fame. In some games, Pokémon can be disguised as fake item balls. Voltorb, Electrode, Foongus, and Amoonguss can all appear in these ways. They do not reappear if the player defeats or runs from them.
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