Stalemate is sort of the offical term for when a game of Chess ends in a Draw … It’s when a player’s King is safe on a square AND the King is the only Piece that player could move, BUT is unable to as it would place that King in “Check”.
Because the King is safe where it is and could remain forever there, without being attacked. Therefore, the game’s rule-makers decided this situation results in a Draw (Stalemate).
Stalemate Rules
There are approximately 5x different rules, or situations, that determine when a game ends in a Draw …
A player can claim a Draw if no capture has been made and no Pawn has been moved in the last fifty consecutive moves (fifty moves by each side).
2) Three-time Repetition of Position Rule
If the same position is repeated three times in a row, the game is declared a Draw.
Promotion to a Queen, without thinking through the result, might cut off all escape routes for the enemy King, except the square that King is on, in which case the game ends instantly in Stalemate.
Kings cannot sit on adjacent squares. Since neither can attack the other, a Draw is declared if only the Kings remain on the board.
If both players determine and agree that the game is heading for a Draw anyway, they can both agree to end the game immediately and share ½ a point each. One player offers the draw, the other player accepts the offer.