How about a "No Man's Land". A bunch of mines, machine gun nests, and a border wall with roving patrols, drones, and helicopters. Anyone who enters the zone is fair game. We can shoot on sight any of the "undocumented migrants", cartel members, gang members, mules, coyotes, or any drunk gringo who lost his passport while partying in Tijuana dumb enough to come within a half mile of the actual border and Mexico could do the same for any of the bad Chad's smuggling US guns into Mexico. In fact, anyone found with a hole in their back just means that Mexico caught them trying to leave before we caught them trying to come in. The country with the most dead bodies from their side of the border at the end of the day is responsible for disposal of the bodies from both sides.
If you want to come in, do it at one of the legal Ports of Entry where you can be checked, searched, prodded, and probed if necessary to ensure you are good to go for entry.
Don't laugh, this system works okay for Kim. Just a couple of days of this and they'll be flying into Canada to try to walk into the country from there. Then comes the Canadian border security suite.
Yes, I take my border security seriously.