The guy is a foreign national. Deportation is an administrative remedy to his having been in the US illegally. If, as a deported foreign national, he feels his deportation was wrong, he can petition the US courts from wherever he is to remedy that matter. He is not entitled to remain in the US indefinitely while awaiting a final decision on that order of deportation.
This is akin to the "Wait in Mexico" policy regarding asylum hearings. You have no RIGHT to entry into the US to await a claim for asylum. You can wait in the first 'safe' country you enter, thus the "Wait in Mexico" policy being legal. Same thing with deportations. Argue that it was wrong from whatever country you were deported to.