Speaking specifically for USSSA, but I'd be surprised if USA is any different.
This should never happen and is not actually covered in the rulebook or casebook.
Here is what I am doing. I'm letting the second run score. No one can convince me that the runner wasn't on the base at the start of the play. The third out is the missing runner. What should have happened is that the umpire should have seen that the batter-runner did not come back to the base, give them a chance to come back but once the ball is pitched and the runner isn't there, it's a dead ball out.
Had something somewhat similar happen at the Las Vegas Conference event last year. Runner on first and batter hits a DBO, runner steps off first and starts coaching thinking the HR counted. Next batter hits a single, and the 1B starts going crazy that the runner wasn't on the bag. Ended up calling the runner out on the pitch for the third out.
Difference between your situation and that one is that the defense told the umpire as soon as the ball was put in play.