They can do audits by precincts to see if the matched ballots match who actually voted. It will just take some work.
I just received a notice to enter a class action suit, for something which happened 4 residence changes ago. I am amazed how they can find me after 20 years. And the letter is not forwarded many times, it had my CURRENT ADDRESS!
Point is authorities know exactly who lives in a precinct and how many are registered to vote.