There are four basic keys to fixing the problem but the public has zero interest. First, national ID card across the nation for citizens only. Second, make it a requirement to show the card if you want to sign a apartment rental deal or rent a hotel room or get any service via anyone. Third, visas are written for 120 days maximum...if you want to extend it...you ask to extend it but you keep putting yourself back into the request mood each time. Finally...put a bounty on each one of these guys who overstay and fail to request a new visa....say $3k in cash to turn the guy in and then accept no reasoning for helping the guy ever again. If you got 100,000 bounty hunters on the streets of the US...we’d eventually fix the problem.
Your “cure” is worse than the disease. National ID my ass.
That's always been my suggestion....except I would require that high-risk individuals post a $10K bond which would provide for a more substantial fee for the bounty hunter and cover administrative costs.