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On the other hand, if player A plays Protector on player B's hero, and player B gets a "discard all attachments you control" shadow effect then the Protector is not discarded.
This is not correct.
When a player plays an attachment card, he has the
option of giving control of that card to another player
by attaching the card to one of that player’s characters.
Players always assume control of attachments that
have been played on their characters. If control of
that character changes, so does the control of any
attachments on that character.
Player B controls Protector of Lorien. Only player B can activate Protector of Lorien. The shadow effect of Driven by Shadow would affect Protector of Lorien if it came from an enemy with which player B is engaged.