If your rights are suspended at the border, then whose rule of law does apply? Clearly not the US, then would it be the neighboring country like Canada? Or is i

If your rights are suspended at the border, then whose rule of law does apply? Clearly not the US, then would it be the neighboring country like Canada? Or is it some sort of no mans land? With more and more of these stories bringing up the lack of 4th and 5th Amendment rights, I'm becoming curious as to what can legally happen at the border. How would common crimes be handled in this area?