Here's one for you

[SideLine]

4th and 14 from the K30, K1 is in scrimmage kick formation, receives the snap
and kicks the ball high into the air, the ball crosses the neutral zone. R1 signals
for a fair catch as he is running towards the ball, a gust wind blows the ball
back behind the neutral zone, while R1 is running to make the catch he runs
into K2 who was advancing downfield. The ball strikes the ground behind the
neutral zone where it hits R1, and the ball is recovered by K3.

[SCHSref]

4th and 14 from the K30, K1 is in scrimmage kick formation, receives the snap
and kicks the ball high into the air, the ball crosses the neutral zone. R1 signals
for a fair catch as he is running towards the ball, a gust wind blows the ball
back behind the neutral zone, while R1 is running to make the catch he runs
into K2 who was advancing downfield. The ball strikes the ground behind the
neutral zone where it hits R1, and the ball is recovered by K3.

R ball.  1st and 10.  R didn't touch the ball beyond the nz and then it was recovered by k.  I might be wrong, but just a cursory thought off the top of my head

[ncwingman]

The fair catch signal was legal since it occurred when the scrimmage kick was in flight. There is no KCI for running into K2 because the ball was then behind the neutral zone at the time of contact.

Assuming the ball stays behind the neutral zone once it hits the ground, the touching by R is irrelevant and the recovery by K3 is allowed -- although the end of run is behind the line to gain.

Result of the play is a turnover on downs, R's ball, 1st and 10 at the spot of K3's downing of the ball. There should be no flags on the field.

[kevinlc]

I think this is a straightforward 1st and 10 for R at the recovery spot behind the NZ.
To throw a wrench in, suppose the play is as described but K-3 kicks the ball after he recovers it behind the NZ and R-2 catches the kick beyond the NZ and begins to advance? Now what do you have?

[AlUpstateNY]

I think this is a straightforward 1st and 10 for R at the recovery spot behind the NZ.
To throw a wrench in, suppose the play is as described but K-3 kicks the ball after he recovers it behind the NZ and R-2 catches the kick beyond the NZ and begins to advance? Now what do you have?

The principle remains the same, when a scrimmage kick has not been touched by R beyond the line, rebounds behind the line K can advance it, pass it or kick it again.  Since R hasn't given a binding FC Signal, he can advance the kick.  1st and 10 for R, at the dead ball spot.

[prab]

I used to laugh at plays where a punt crosses the LOS and "is caught by the wind and blown back behind the LOS", until I had it happen in a Freshman game a few years ago.  In our play, the ball was blown back into K's end zone and went out of bounds there, resulting in a safety.  So, although plays like the OP are unlikely, it doesn't hurt to consider them from time to time.