Nafta allows them to stay and visit even when they lose their H1 visa. They can't work of course, unless they find another H1 sponser. But they needn't leave either.
The department told the GAO that it is in the process of changing the systems used to track the foreign workers.
Guess who is changing the systems (I bet)? :>)
On a real serious matter I ran across another government report about national security issues of exporting technology. While there are some rules for exporting technology there appears to few rules for using H1B workers where they acquire knowledge that effectively transfer forbidden technology when the workers return to their home countries.