It means they need to run more, longer trains.
Sold out trains still sell standing tickets, which let you pick seats if available. I've seen old ladies choose to stand so they can all be in a group.
Also sometimes they're not totally sold out, but you'll be choosing between a standing ticket and an expensive first-class ticket or hard seat and soft-sleeper for a slow train.
They do hand-counts when there's an irregularity.
Hand count consists of 1 delegate from each party tallying every single ballet. If they disagree on a ballet (this is less common if a computer prints the ballet), an official agreed on by both parties determines what the voter intended.
The voting system is quite good by international standards, the fix in American "democracy" comes in way before all of this.