The ball becomes dead when: it settles finally with the keeper or bowler, a boundary is scored, a batter is dismissed, it lodges in a player's equipment, or the umpire calls over/time/dead ball (e.g. serious injury, or the batter not ready). The ball is NOT dead just because it hits the stumps without a dismissal — overthrows off the stumps stay live and batters may keep running. A keeper catching a missed ball does not instantly kill it either; byes can be attempted until the ball is settled.
Related: death overs decent length Declaring an innings declared
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