I am not aware of any such plugin existing, it sounds pretty specific, but there might be something in the plugins database.
If I was tackling this, I'd probably look to create an authentication plugin, based on whatever form of authentication you use already, but adding in the check for a user having failed the test and then denying them access until they paid (whether that was on automatic online transaction, or a manual re-enabling process).
I would also include an event handler, that would catch the 'quiz submitted' event, check to see if it the quiz matched (one of) the configured quiz(es), then call user_logout if they did not succeed (might need a bit of care, so as to not break any other event handlers, if the user suddenly stopped being logged in).
If you've got PHP developers on hand, they should be able to put something like that together for you.