The period is not extended for an untimed down because the penalty includes loss of down. If the remaining time elapses before the snap, the period is over.
Right. But if a smart coach instructed the players do something in this situation that is NOT a loss-of-down penalty, the team gets the next down regardless of if they get the snap off before the end of the game.
For example, after the player is across the line of scrimmage, the player punts the ball into the endzone where this 'illegal kick' is caught (fumble recovery as an illegal kick is treated as a fumble). This is not a loss-of-down penalty, so the team would be able to get the next play off, correct?
I'm not advocating that this is a good play (because kicking through the back of the endzone (fumbling) is a turnover. But, I'm just stating that this is a loophole in the rules.