When caught the illegal should be tagged with a micro-chip. In this manner we could track them if they return again. The micro-chip can be activated at anytime and have a GPS locator.
That sounds good to me but is eerily a reminder of the "mark of the beast" coming in the "latter days"
Also, a new industry would be formed, coyotes would perform border surgery to remove "chips" - for a fee.
But, you are thinking outside the box and that is what our government cannot do.