Can magic be undone without being found, or must it be present for it to be nullified? And is it permissible to dig up a grave if we are absolutely certain that magic is buried there?

There is no need to extract magic to undo it; rather, it can be undone with ruqyah and supplications. The Prophet's magic was undone with the Mu'awwidhatayn without extraction. Therefore, it is not permissible to exhume graves to extract magic, because exhuming graves is not permissible except out of necessity, and undoing magic is not one of these necessities.