Hmm... This is tricky, but I have thought of a way. I'm not sure if it's the best way.
But you could run a query on your MySQL database that automatically populates that custom field where it is currently empty with some sort of string, such as "FILLMEIN"
You can then set up a User Group Promotion that says if your custom field contains "FILLMEIN" then they should be added to a usergroup that essentially blocks them from doing anything. You could put up a notice on the front page that displays a notification to anyone in that Usergroup with the instructions they need to take to restore their access.
The next time the User Group Promotions cron is run, they should be removed from that group again.
It's one way - not the way. I've just tested it on my test board and it works.