Greymule:
I don't know anything about the softball rules.
The "awards" half of the play is easy: It's the same at FED, NCAA, or OBR:
When a runner has left a base too soon (always obvious to everyone), if a subsequent throw by a fielder goes dead, the runner receives two bases measured from the base occupied at the time of the pitch.
The "baserunning" half (when may he retouch without penalty) of the play is different at every level.
If it is a FED game, the runner may return to touch the base and then receive his award. But if he had touched (or was beyond) a subequent base at the time the ball becomes dead, on a timely appeal, he would be out.
If it is an NCAA game, the runner may return if he had started back by the time of the throw.
If it is an OBR game, the runner may return unless he has advanced and touched a base AFTER the throw because dead.
Ain't baseball grand?