Assuming they came from Eastern Europe or Africa, got caught by US immigration, but gave up no information, how would they know where to send them back to? Does ICE have a department that investigates this? I'm sure it's a pain in the butt.
Let's say the person is Australian. Would they actually have to prove they were from Australia first before sending them back? What if they were really from New Zealand, Ireland or the UK, you know? I'm not sure they could actually decide based on the accent.
Or do they just get away with it and get to stay? Always wondered about this.