If your time is up on a timed game, but your opponent has only a king, the game is drawn.
Does this rule apply to online correspondence games?
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Note: This was answered before the OP edited the question, and specified it was an online competition.
According to ICCF (international) rules, yes, it is still a draw.
6.7 Except where one of the Articles 5.1 or 5.2 applies, 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.
The USCF rules are more convoluted. First, there is a special rule 11 in national events that if someone oversteps the time limit, they are not forfeited, but rather penalized five days reflection time on the succeeding 10 moves/30 day time control. They lose the second time this happens. (Plus there are entire sets of rules for specific national events linked on that page)
Otherwise, they also follow the traditional USCF rules of chess, so yes, it would also be a draw in that case too.
14D. Insufficient material to continue. The game is drawn when one of the following endings exists as of the most recently determined legal move, in which the possibility of a win is excluded for either side.
14D4. No legal moves leading to checkmate by opponent. There are no legal moves that could lead to the player being checkmated by the opponent.