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The rule is this: ''The game is drawn when a player having the move claims a draw and demonstrates that at least 50 consecutive moves have been made by each side without the capture of any piece and without the movement of any pawn.'' -- From the FIDE Laws of Chess
<p>In other words, if no one has made a capture or moved a pawn within the last 50 moves (by each player), then the game is a stalemate.
<p>There is no rule with regard to one player having their King as their only remaining piece, although that is typically the situation in the above rule.
<p>I hope this answers your question. If not, please keep asking!