What stops a fillibuster?

Answer 1

In the United States Senate, the rule used to stop a filibuster is called "cloture." With the approval of three-fifths of the sitting Senators, this rule sets a limit on how long the Senate can continue to debate a bill or other proposal before voting on it.

Answer 2

A filibuster can be stopped by a motion for cloture which requires 60 senators to vote to end the debate. A filibuster also ends when the one doing the speaking sits down.