"The border" represents that we have a Bill of Rights which is merely an outline of our Natural Rights. Nowhere do Natural Rights imply or demand that people be "documented" or have a "Green Card" to come and/or go. If one is suspected of or commits an actual crime against person or property, they have the right to face their accuser in a court of law before a jury.
Perhaps I am the exception - in this day and age.
Crossing of the US border without authorization is a crime.
Cross the border into Mexico without authorization and see what happens to you.