Ball Fetch
If the Pokémon is not holding an item, it will fetch the Poké Ball from the first failed throw of the battle.
Full effect
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.
In game description
If the Pokémon is not holding an item, it will fetch the Poké Ball from the first failed throw of the battle.
Pokemon with Ball Fetch
Using Ball Fetch in Cobblemon
Abilities are passive and always active, so Ball Fetch costs you nothing to run. If it is marked hidden on a species above, expect it to be harder to obtain: servers differ in whether hidden abilities come from breeding, an Ability Patch, or events.
See the Pokedex for which abilities each species can have, and IVs, EVs and breeding for how to actually pass one down.