Who wins in a stale mate?

In Chess

A stalemate is a condition in which neither side can win, and so it is when it ends a game of Chess. If the player to move cannot make any move without putting his king into check (jeopardy of being taken) and the King is not already in check, it's called a "stalemate." It's considered a tie game.

Stalemate has also become a widely used metaphor for other situations where there is a conflict or contest between two parties, such as war or political negotiations, and neither side is able to achieve victory, resulting in what is also called a dead heat, standoff, or deadlock.

In this usage, unlike in chess, "stalemate" often refers to a temporary impasse that may ultimately be resolved.