What is the outcome when a second baseman allows a fair fly ball to drop untouched with one out and a runner on first base?

When a second baseman allows a fair fly ball to drop untouched with one out and a runner on first base, the play is considered live, and no one is out at that moment. In this scenario, allowing the ball to drop does not constitute a catch, therefore the ball remains in play.

The defensive team still has the opportunity to make a play on the runner at first base, who has the option to advance. Since the ball is live, any subsequent actions—like throwing to a base or fielding the ball—can lead to the runner being put out or legally advancing bases. It's important to note that if the second baseman had caught the ball, the runner would have to tag up before advancing, but since the ball was not caught, this scenario does not apply.

Thus, the correct interpretation of the situation is that the ball stays live, and no outs are recorded until a play is made.