If the Pokémon is not holding an item, it will fetch the Poké Ball from the first failed throw of the battle.
At any time after the first Poké Ball is thrown and fails to catch a Pokémon, at the end of a turn, if a Pokémon with Ball Fetch is on the field and not holding another item, it will pick up the same type of ball as the first one thrown.
1 Pokemon can have this ability
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2 Pokemon