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A "POA" is the document that allows the principal to designate their attorney-in-fact and state what powers the AIF has. Typically, an attorney-in-fact can do almost everything the principal him/herself could do, as long as there are no restrictions state in the POA. However, an AIF can never make a sworn statement for the principal. The AIF can only make statements they themselves know to be personally accurate.
Your question is rather vague. What exactly do you mean by document subscriber? Anyone who signs a document is a subscriber. ("Subscribe" means to "sign" or affix ones signature.) Thus, if the AIF has the authority and power granted by the principal, then they can be a document subscriber on behalf of the principal.