Abdicating is an action that a person chooses to do, and that person is very likely an adult. It is not an action that is done to you. So if you see a sentence that says that the boy was abdicated, it is a safe bet that abducted was meant.
Monday Muddle: abdicated, abducted
abdicated: (past participle of verb to abdicate) gave up or renounced one’s duties, position, or power abducted: (past participle of verb to abduct) kidnapped; taken away by force