Session Lock vs Logout

I have an idea that might be a feature request for this module or it might be a new module idea, not sure really if it needs to go that far. What would be awesome would be if the system could suspend the user so that they would be forced to re-enter their password but not actually log them out. Think of the way Windows has a screen saver with the screen lock option. Once the screen saver pops up you have to re-enter your password again to resume your session. That is what I am talking about but in a Drupal/web sort of way.

This is (in my case) for a shared workstation environment similar to a classroom. It might go something like this...

User A logs in and starts using the website, then gets called away from the room by an instructor needing to discuss something. MODULE is set to timeout after 2 minutes of activity. A few minutes later User B comes into the room and sees an empty seat and sits down. Instead of a homepage User B sees a sort of splash page (a locksplash page?) with a request saying "User A, please enter your password to continue" and also saying "If you are not User A click here to end User A's session and start a new one."

Any attempt to bypass this screen such as deliberately entering a known path would be rejected because every page would have a hidden bit of PHP code in the header that would redirect to the locksplash page based on a $_SESSION variable.

PS: I realize the first locksplash page would be a javascript construct but once the user clicks anything it becomes fully server-side driven.