There were lots of examples where themes from a cancelled show would show up as prize music on another of that company's shows. '78
Jeopardy on
Wheel of Fortune is a great example; and another famous for this would be Chuck Barris. Looking at the CD of game show themes from his shows, many of the prize cues actually were supposed to be themes from other shows/pilots. Interestingly, when one of them aired on GSN, the theme wasn't the same as the CD said (ooops!)
There are other cases where a show would only have one piece of music, and different parts of it would be used for different cues.
Now You See It '74 would seem to fit (although they did add that second unidentified piece as a closing theme early in the run and used that thereafter for some commercial cues).
Tattletales in '74 used the end part of the theme for audience prizes (heard in a couple of studio master episodes floating around), and
Wheel of Fortune used the end of "Changing Keys" when someone solved a puzzle for a few years after making that their main theme. I didn't even know it was the end until the entire theme played over the credits in an '84 episode (long before we had it on CD).
As for who makes these decisions, don't know for sure but I would imagine the show's music director/co-ordinator would have a say in it. After all, that's one reason they were hired, right?