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Their poverty is established by the arrangement of the text.
In the Hanafi reasoning under discussion, calling the emigrants “poor” indicates that they no longer effectively possessed the property from which they had been displaced. That is not the direct object of the distribution clause, but an implication drawn from its description.
The right to receive distributed property and the persistence of prior ownership are separate legal questions, reached by different textual routes.
This is analysis of a historical jurisprudential example, not a blanket present-day permission to seize another person’s property or a statement of contemporary rules of war.