I heard that they lose some time or that they lose the game. I'm not sure what happens.
By the FIDE Laws of Chess, article 7.4:
- a. If during a game it is found that an illegal move, including failing to meet the requirements of the promotion of a pawn or capturing the opponent’s king, has been completed, the position immediately before the irregularity shall be reinstated. If the position immediately before the irregularity cannot be determined the game shall continue from the last identifiable position prior to the irregularity. The clocks shall be adjusted according to Article 6.13. The Articles 4.3 and 4.6 apply to the move replacing the illegal move. The game shall then continue from this re-instated position.
- b. After the action taken under Article 7.4.a, for the first two illegal moves by a player the arbiter shall give two minutes extra time to his opponent in each instance; for a third illegal move by the same player, the arbiter shall declare the game lost by this player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves.
That is, on the two first illegal moves of your opponent, you gain time on your clock (two minutes, which likely does nothing), but on the third illegal move of your opponent, they lose the game (unless it was already impossible for them to lose it).
When it comes to Blitz games (5 minutes or 3 minutes + 2 seconds) first illegal move loses the game on the spot. Other solutions (like adding 2 minutes) would lead to total confusion.
Keep in mind, after your oponent has made an illegal move, you are obliged to:
- stop the clock
- call the arbiter
- explain what happened
(btw, you must have time on your clock, if you are already at 0:00 then you can't do anything)