There is another Bounty radio ad that does the same with "The Pina Colada Song".
The song dies down when it's implied that the unseen person spilled their red wine but after they are told to use a Bounty paper towel to clean it up, the song picks back up.
Occasionally, a non-musical variant is used in science-fiction movies involving marauding robots and world conquering computers. And because (as suggested above) sometimes the music is non-diegetic and therefore wouldn't necessarily stop instantaneously. Yet it persists due to The Coconut Effect. Ostensibly, this trope shouldn't be played straight anymore because most (if not all) music players these days are digital, and when you pull the plug on a digital player, the music just stops abruptly (sometimes after a short burst of unmusical noise) rather than just fading. Sometimes the two tropes are used together. Instead of swiftly pulling the needle across the record album, the people running the Background Music pull the plug on the record player, allowing the turntable to slow until it finally stops rotating. Letting the Air out of the Band is a variant of the Record Needle Scratch.