Doesn't this appear pretty much any time a song is written for a work? For one thing, not having enough song for the scene would kinda be a problem, so they have to make them to long. The inversion seems more interesting (when the whole song is
Seems like the audio version of a directors or extended cut to me.
Directors Cut Songs
Extended Cut Song
I'm not sure how you define this so people won't use it to complain that songs they like were cut down.