Does the run count?

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Situation: Runner on third, two outs, 2 strikes
During the pitch, runner breaks for home to steal. Runner slides in home safely. Pitched ball is called strike three but catcher misses it. Batter has stepped out of box after pitch goes by to allow runner to slide home. Batter does not attempt to get to frist on the dropped third strike, but walks toward dugout and is called out.
Question: Does the stolen base and run scored count? Opposing coach arued no, because the runner did not safely get to first base (as on a batted ball that results in the third out). I said yes, because the run scored before the third out was recorded on a non-batted ball.
Did either one of us properly apply the rules, or does some other rule apply here?

 

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No run.

It would be the same as though she put the ball into play and was thrown out at first; even if the runner at third touches home first, no run is scored.

 

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Agree- no run.

No run can be scored when the the third out of the inning is a result of a batter-runner being called out before reaching first base.

The batter becomes a batter-runner not only on a fair batted ball, but also on a walk or uncaught third strike (in situations where she is entitled to run).

In the baseball world, this run might count if the runner from third touched the plate BEFORE the pitcher made any motion to deliver the pitch. That would be an exceedingly rare circumstance.

In softball, it is an impossibility. The runner cannot leave the base before the pitch is delivered.

Having said all that, from the description of this play the umpire may have called the out prematurely. The batter-runner is not out UNTIL she actually steps into dead ball territory (the dugout). She could walk toward the dugout, come within an inch of stepping into it, then make a dash for first base. The defense would still have the responsibility to complete the put out. If they did not, the batter-runner could safely achieve first and the run would score.

Was she called out as she was walking toward the dugout, or after she stepped into it?

 

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A lesson to be learned here - on an uncaught 3rd strike, teach your catcher to never assume an out being called. The catcher should ALWAYS scramble after the ball and either tag the runner (even near the dugout), or throw down to 1st base for the put out. Then you leave no doubt. Rec ball leagues usually don't have the uncaught 3rd strike rule, so some kids forget to run from habit.