What often happens in Europe is that you are illegally deported however. Often an asylum claim is illegally dismissed by authorities, a person has a right to a hearing but is deported before they have a chance, a person is sick and is not allowed to be deported under some conditions etc. A person may have entered using a fake ID, however this is still not a crime if they are fleeing, as official IDs are not something one can easily get when fleeing ones home, and the law most often reflects that (but is then broken by the authorities).
When you hear about what refugees have to go through in the real world you would be surprised by how little authorities abide by their own law and how easily they are willing to break their own laws to evade helping people that need it.