An ability that certain Pokémon have allows those certain Pokémon to find certain items after a battle. Firstly, Here's a List of all Pokémon With This Ability:

Now these are the items which can be found. There are rumours of other items being found i.e. Masterballs but don't count on it

Item Rarity Use
Super Potion Common Restores 50 HP
Ultra Ball Uncommon Captures Pokémon at a x2.0 rate compared to Pokéballs
Full Restore Uncommon Cures all status conditions and restores all HP
Full Heal Uncommon Cures all status conditions
Nugget Uncommon Sells for a High Price
Revive Uncommon Revives a Fainted Pokémon and restores ˝ of its HP
Rare Candy Uncommon Raises a Pokémon One Level
Protein Rare Increases a Pokémon's Attack
PP Up Rare Increases a Pokémon's Attack PP
King's Rock Very Rare May cause flinching when oppenet is hit. Evolves Slowpoke into Slowking & Poliwhirl into Politoed when held and traded.

 
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