Runners on 2nd and 3rd with 1 out. Batter hits a fly ball to right center field. Center fielder catches fly for the 2nd out. R2 and R3 tag R3 scores and R2 moves to 3rd base. Other team appeals R2 left early. R2 is called out on appeal. Does R3 score?
Yes the run scores.
R2's being retired for the third out is a timing play. Clearly, R3 scored before R2 was retired.
It is a common misconception that a runner who fails to tag up properly is a force play. ("He's 'forced" to go back!") Not so! A force play is ONLY a case where a runner must vacate his base and attempt to advance as a result of the batter becomming a batter-runner. IOW, a ground ball means the batter must try to run to first, and all runers forced must vacate thier bases and attempt to advance. (Other kinds of plays can happen, but those are the basics.)
A runner who is off the bag when a fly ball is caught--and who fails to tag up--is vulnerable to an appeal play: either it's the classic "he left early" appeal, or it's a continuous action appeal, such as when a line drive is caught by the second baseman and the throws to first to retire R1. In either case, the context is an unmistakable apppeal on a runner's violation at th correct base.
So since your R2 was not retired on a force play, the run scores on timing.
[EDITED TO ADD:} There ARE running violations--such as R1 missing second base on a ground base hit--where the FORCE is still in effect on the appeal. If that were the case on out #3, then no runs score.
But . . . . . .
Here's an important rule to remember. You could have a 4th out in a related situation.
Assume, in your situation, that both runners left early, or that R3 left early and R2 tagged up but then got tagged out in a rundown.
Even though R2 is the 3rd out, the defense can still appeal that R3 left early, which would be the 4th out, but they would do so to prevent the run from scoring.
Even major leaguers forget this rule, and somebody in the last couple years (Dodgers?) gave the other team a run by not knowing the 4th out appeal rule.
[Never mind. Read Mike's reply. This might be correct, but his is better.]
Yes, the run scores.
Most people who ask this question know that a run can't score if the third out is a force. They tend to belive that any time you can put the runner out by tagging the base, it's a force. This is incorrect.
A force play occurs when a runner loses his rights to a base because the batter became a runner. When the batter-runner is put out (when the fly ball is caught), all forces are removed. So an appeal out for failure to tag up is NEVER a force play.
So, yes, the run scores.