Ministry deputy chief executive Mike Smith said the agencies were "now taking steps to share information that will close this anomaly".
"While these cases are extremely rare, it is important agencies share information where people are no longer entitled to benefits because their residency status has changed."
Internal Affairs revoked two citizenships a year on average, and not all would be getting a benefit, he said.
Associate Social Development Minister Chester Borrows said he was satisfied the departments were "moving at speed" to close the loophole.
Al-Bawi, who came to New Zealand in 2000, received nearly $24,000 in legal aid for a series of court cases, including to keep his refugee status and to fight criminal cases, including his bid in the Court of Appeal to overturn his immigration convictions.
He no longer has a New Zealand passport and has been refused re-entry, despite having a young son here with his former partner. The ruling means he is stateless.
Further inquiries reveal he remains a 99 per cent shareholder in an Auckland car parts import-export business.