Each Pokédex has a holder registration system, meaning when it is assigned, the holder must register their name and fingerprints, which means each of the Pokédexes is only allowed to have one rightful owner. However, it is possible to transfer data from one Pokédex to an upgraded version, leaving the Pokédex that had its data transferred with no rightful owner, and thus, the Pokédex would be able to be reassigned to a new owner.
In the FireRed & LeafGreen arc, Professor Oak asks Red, Blue, and Green to return their Pokédexes to him, so that he could upgrade them to National Pokédexes. Though in the process, they get stolen by Orm and used by Carr to create a "black Pokédex".
In Pokemon Adventures, each Pokedex is assigned to a person, and the only way to unassign a Pokedex to someone is before it gets reassigned after an upgrade. If a Pokedex gets stolen before a user has been assigned or reassigned, they can register themselves to use the Pokedex.
There has been no instance of a registered Pokedex being stolen to be used in the anime or games, so this is the best answer available at the time to the community. However, it would be safe to assume it would be similar in the games and anime, as the Pokedex's have been used as an ID for the holder.
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