I had this (sort of) happen last night in my JV game, and I thought about this thread as soon as it happened.
It's 1st and 10, A runs and loses two yards. After the play, the 3rd quarter expires. The box has moved to the correct position, but never flipped the down, so it still said 1 and not 2.
Technically, by rule, by the case play, since the R held the ball up to signify the end of the quarter with the box still saying "1", the next play must be 1st and 12, since it is too late to correct the down.
In reality, as we flipped the chains, I told the box guy "We're playing 2, not 1" and he flipped the box and nobody cared or probably even noticed. I don't know it might matter that the ball wasn't ready for play in the 4th quarter with the box being incorrect, everything was fixed during the 1 minute intermission.