From Bulbapedia, the community-driven Pokémon encyclopedia.
Snagging (Japanese: スナッチ Snatching) is a method of stealing captured Pokémon. It is used by both protagonists and antagonists in Pokémon Colosseum and Pokémon XD: Gale of Darkness. Team Snagem snags Pokémon from their Trainers and gives them to Cipher so they can be converted into Shadow Pokémon. Conversely, Wes and later Michael will snag the Shadow Pokémon Cipher has created and purify them back into normal Pokémon.
To snag a Pokémon, the thief needs a Snag Machine and any sort of Poké Ball. The thief then enters a Pokémon battle with another Trainer. The Snag Machine will convert the normal Poké Ball into a Snag Ball, which the thief then throws at the other Trainer's Pokémon. This Snag Ball ignores that the Pokémon has already been captured and attempts to capture it as if the Pokémon were wild. If successful, the Pokémon becomes the property of the thief, and there is virtually nothing the other Trainer can do about it. Some more oblivious Trainers may not even realize what had happened, believing that it was some odd trick, and may think that they just misplaced their Pokémon.
Presumably, this is not the only method of stealing Pokémon. Pokémon thieves are comparatively commonplace, particularly among criminal organizations like Team Rocket. Even in Pokémon XD: Gale of Darkness, Miror B. steals Shadow Pokémon from Cipher despite having no Snag Machine. However, it can be assumed that all other stealing methods are of the Poké Ball itself, rather than the Pokémon, or otherwise an unfair acquisition of Pokémon without Poké Balls. The Snag Machine is currently the only specific method of stealing a captured Pokémon known.