This is how it’s done by US INS. Anyone who cannot prove she/he is an American citizen will be issued a removal order. This requires that person to leave the US, usually within 10 days. The INS simply detains that person in custody for 10 days and then requires they board a plane to Mexico (or wherever is their nation of origin). Generally, the person being removed is allowed to select that nation. Now what happens when that person deplanes in for example Mexico without a Mexican passport is not the INS’ concern. This is one of the ways refugees get bounced around from one country to another. The INS can also remove non-citizens by force. This usually involves being handcuffed to a seat in a plane or a bus.