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.