What you are talking about sounds like tri-state problem.
The checkmark has been set == 1
The checkmark has been unset == 0
The checkmark neither been set nor unset == third state.
One way to store this third state in a DB would be allowing that column to be NULL.
You could check for this like so:
SELECT *
FROM MyTable mt
WEHRE mt.TriStateSomething = NULL
Cheers!