A sack. For example: "Although the quarterback scrambled to get out of the pocket, he just couldn't avoid the sack."
It's a sack as long as the QB is on his side of the line of scrimmage. If he crosses the line, it becomes an ordinary tackle.
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Tackling can be dangerous, and quarterbacks are usually very valuable players. This is the same reason why many quarterbacks will run out of bounds or slide down when running with the ball to avoid a tackle.