In a sudden death time control (players have a limited time to play all of their moves), if it is discovered that both players have exceeded their time allotment, the game is a draw. (The game continues if it is not a sudden-death time control.)
If only one player has exceeded the time limit, but the other player does not have (theoretically) sufficient mating material, the game is still a draw. Law 6.9 of the FIDE Laws of Chess states that: "If a player does not complete the prescribed number of moves in the allotted time, the game is lost by the 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, even with the most unskilled counterplay." For example, a player who runs out of time with a king and queen versus a sole king does not lose the game. It is still possible to lose on time in positions where mate is extremely unlikely but not theoretically impossible, as with king and bishop versus king and knight.
Because of this last possibility, article 10 of the FIDE laws of chess states that when a player has less than two minutes left on their clock during a rapid play finish (the end of a game when all remaining moves must be completed within a limited amount of time), they may claim a draw if their opponent is not attempting to win the game by "normal means" or cannot win the game by "normal means". "Normal means" can be taken to mean the delivery of checkmate or the winning of material. In other words, a draw is claimable if the opponent is merely attempting to win on time, or cannot possibly win except by on time. It is up to the arbiter to decide whether such a claim will be granted or not.