Runner from second rounds third on hit and crosses commitment line. He sees the throw and decides to go back to third. Duh. Pitcher cuts the throw and not realizing the runner had crossed throws to third. Overthrow. The runner now scores. Is he safe? Or is the runner out as soon as he re-crosses?
If the call is made correctly, he is OUT upon re-crossing the commitment line for any reason headed back to 3B ... See Rulebook §8.8 • COMMITMENT LINE on page 52 ... He's called out and the ball remains live (well, at least until the wild throw goes out of play!) ...
LMR, that runner is out rightvwhen he recrosses the commit line going back to third.