LHSAA 5A Championship Game
 

I was watching a replay of the Louisiana 5A championship game last night. R2, U2 at 3B, U1 between 1B and 2B, not sure of outs, three man crew. Batter hits a fly about halfway between 3B and the foul pole right on the line. U3 is backing perpendicular to the foul line away from 3B. I couldn't see the PU to know what he was doing. The TV announcer sounded surprised went the runner's countinued to run as no one signaled fair/foul. Was U3 correct in what he did? What is the correct rotation in this situation?

I think you are saying a runner at 2nd, maybe 1st also.
Unless there was a specific exception, U3 goes out for the ball, PU has lead runner into 3rd and the tag at 2nd if a catch.

Runner at 2B only, R2

Then the correct nomenclature is R1 at 2B.

OK, so if I read correctly, you saw U3 "chase". But the chase you described is different than what I would expect. I would expect U3 to be chasing on the line as he/she goes toward the play.

U3 did not chase. He backed away from the third base line facing toward third base. That's what I'm asking, shouldn't he have gone out to make the fair/foul call?

OK, now I understand your question - should he have chased.
It meets the criteria I use to determine whether or not to chase.
I use:
1-a ball on the line
2-a ball to the wall
3-a fielder charging in
4-a fielder charging out
5-multiple fielders coming together

For your play - see #1.

1) Initial decision by U3 not to chase probably wrong.
2) Since U3 didn't chase, he did the next best thing, he cleared the line so PU could see. PU now responsible for fair/foul; since you didn't see him, I wonder how you determined "no one signaled fair/foul"?
3) With U1 counter-rotated, U3 doesn't rotate to 2nd on this play. His next play, if any, is B3 into 3rd.

Just made a guess on the fair/foul signal. The TV announcer sounded very surprised that the ball was fair. It seemed from his comments that he figured the ball was fair because no one was stopping the runners from advancing.

Well, that's a matter of opinion.

It's really a matter of the organization responsible for the game. I assume this was a high school game, and I further assume it was played under NFHS rules (some states use other rule sets for high school ball, so I'm not certain). NFHS uses the the naming convention of runners where R1 is the leadmost runner, R2 is next, etc., in its case book.

Not sure which softball organization calls R1 the runner who starts on first base, R2 starts on second, etc. I see that mostly in baseball circles.

Given the OP and that the PU is expecting to cover 3rd if U3 did the expected chase; should the PU communicate to U3 at some point and if so, how? Is just "I have home" when leaving 3rd with R1 enough of a clue?

It's not. Not in softball at least. (In baseball, it's not a matter of opinion but rather a matter of ruleset).

I saw the game on replay a couple of weeks ago and saw the play in question. U3 should absolutely have turned and taken a look at that ball. That is his responsibility every day, all day. He screwed up deciding not to chase, but it happens. What I didn't like was his bailing nearly to the fence. Not sure what set of mechanics calls for that but it's not the first time I've seen it at all levels. I never understood it.

On a ball hit that far down the foul line, there's absolutely no reason for U3 to do what he did. It's not as if the ball was a bloop pop up right on top of him, and he had to bail to avoid F5, F6 and F7 converging. He should have simply turned around and taken responsibility for the Fair/Foul and Catch/No Catch calls. And if he were to give up that responsibility to the PU, then he should have come inside to watch R1 touch third, and take all calls at third base.

From your description, he did neither, and left the other umpires at two-man, forcing the PU to watch for the Fair/Foul and Catch/No Catch, and to take responsibility for R1 going into third and home.