What would happen if a game lasted for more than 24 hours? Technically it is possible for a game to last more than 24 hours, since after 40 or 60 moves each player generally gets a 30-second increment.

In an endgame, the player with the advantage will just need to be careful of the fifty-move rule and the threefold repetition rule, and he would be able to keep pressing for many many hours hoping that his opponent will crack and make a mistake.

But the problem is: 24 hours after the game has started, the next round would need to start!

So what would happen?


Would the entire round be delayed for everyone participating in the event?
Would the next round start normally on time for everyone, except for 4 players (including the 2 players playing the problematic game) who would need to wait for the problematic game to end?
Would the next round start normally on time for everyone, and the two players who are still playing the problematic game would need to play their next round games while simultaneously continuing the problematic game?
Would the arbiters simply decide to end the problematic game, considering it as a draw?
Would the FIDE President need to add a new rule to prevent this kind of situation from happening again?
Although replies by Brian Towers and StudentT are the right ones (both players would be disqualified) from a theoretical points of view it would be possible that a game has not ended in time for the next round to begin. I would even say that it's possible that it could actually happen in a tournament with 3 rounds per day.

I case it would happen I guess the game would be adjourned by the arbiters. The entire round would not be delayed/cancelled, but the result would be considered to be a draw for pairing purposes only. See General handling rules for Swiss Tournaments, point D.1, and Laws of Chess, point E.1.a.

From Laws of Chess


  If a game is not finished at the end of the time prescribed for play,
  the arbiter shall require the player having the move to ‘seal’ that
  move. The player must write his move in unambiguous notation on his
  scoresheet, put his scoresheet and that of his opponent in an
  envelope, seal the envelope and only then stop the chess clock. Until
  he has stopped the chess clock the player retains the right to change
  his sealed move. If, after being told by the arbiter to seal his move,
  the player makes a move on the chessboard he must write that same move
  on his scoresheet as his sealed move.


from General handling rules for Swiss Tournaments


  Adjourned games are considered draws for pairing purposes only.


Update: I've found a real example in a Catalan tournament (Masdenverge). You can read tournament rules here: http://www.escacsmasdenverge.com/. It was an U-2200 tournament (to allow a 60+30 time control) and three rounds per day were scheduled. See the note where this possible problem is mentioned:


  NOTA: Si una partida s'allargara en excés, superant l'hora prevista
  per a l'inici de la següent ronda, l'àrbitre principal podrà segons el
  seu criteri, emparellar amb el resultat provisional de taules, a
  l'efecte de que els altres participants puguen jugar la ronda següent.
  Quedaran ajornades les partides dels jugadors que estiguen jugant la
  ronda anterior i una vegada finalitzada, s'unixen a la ronda.


A free English translation:


  If a game lasts for too long, exceeding the scheduled time for the
  start of the next round, the main arbiter may at his discretion,
  proceed to the pairing with the interim result of a draw, to the
  effect that the other players can play the next round. Games of the
  player who are still playing the previous round will be delayed and
  once these games end they'll join the current round.


As you can see in this case the draw for pairing purposes rule is used, but games are not adjourned but the players will continue to the end, and then they'll join the next round.