blackpirate, no, this is not possible. The only way to make a somewhat-closed website is to change everyone's group to "Administrators" and putting the website in maintenance mode. But I don't think you would want that.
One solution would be restricting the access to the website to the Verified (or other) group only. So the Users (default group) will not have access to it. Then you could do a weekly purge using the mass users removal tool (but be careful with it).
Note that this also means you would have to move the already existing users to the new group. This is another field where the Mass transfer/removal tool could be useful.
hey i'm joe and i do not work for the company anymore, please contact other staff or tech support
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sometimes i lurk here