The stolen Poké Ball glitch is a glitch that occurs during the last Looker Agency mission in Pokémon X and Y.
In the Secret Lab of Lysandre labs, there's a desk that sits in the upper-left corner. One of the chairs near it is surrounded by Poké Balls, and the other is accessible. Sitting down in the accessible one and interacting with the table will yield an "It's someone's Poké Ball" message. The message usually appears when the player interacts with one of the other Poké Balls. However, it appears when that particular desk is interacted with, even without a Poké Ball on top.