Question

Can Thief successfully steal an Air Balloon?

Answer 1

No.

It is actually not possible to steal an Air Balloon through moves such as Thief and Covet, according to this.

Though Covet and Thief normally obtain items from the foe, they cannot be used to obtain an Air Balloon because they will pop it first.

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Gives the holder immunity to Ground-type moves, but pops when the holder is attacked. Indirect damage will not pop the balloon, and neither will Ground-type moves used against the holder.

-Bulbapedia

As it says, it pops upon being attacked, and if it has already been popped then logically it cannot be used again, and Game Freak likes to use this kind of logic. For example, when using Knock Off on a Pokémon holding a Rocky Helmet, the user still takes damage because they have to touch the opponent to do so.

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Proof

Comments

That's not proof. Thief can hit and fail to steal an item.

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As long as Thief hits, you will always steal the item unless the target is not holding one or you already have one.

Answer 2

It can successfully be stolen

Comments

so it does not pop

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Yes it pops but it can be stolen