Why does everything have to be drama here? You've given us minimal info to help you with, therefore, I can only say that it's no big deal if "this person (again it's a long story)" takes a border run to the states. You're supposed to turn in your form, but depending on which border you go to, you may not even find the office. So you cross the border, nothing will happen, and you cross back in. Nobody cares, not even the American border guards.
Now, if "this person (again it's a long story)" can't actually get themselves onto a bus and up to the border, then you pay a fine at the airport. However, if "this person (again it's a long story)" flies out before 8am in the morning when immigration opens up at the airport (DF airport), then there's nothing the airline can do about it and they let you get on the plane. Unless things have changed in the past 2 years.