But now I'm thinking there is no single musical construct that by itself says "story conclusion."
Rather, it probably has everything to do with the other emotional content of the music, and whether that complements the story being concluded.
Another friend, more musically-trained than myself, suggested perhaps songs whose melodies never veer far from the melodic root
The example I had just played for him, if I remember correctly, was Dirty Work by Steely Dan -- used as the closing music to some episodes of the Longform podcast.
Here's my brother's first stab:
The piece in question may have a sense of development or "completeness" to its themes and structure that denote a finished arc, without actually taking us through one. Similarly, "Beginning" pieces may set up certain motifs without maturing them to satisfaction.
It's a subtle miss to the question, though; "finished arc" and "matured motifs" have no definite meaning in music theory; the phrases used ultimately describe impressions and not specific musical constructs. So it's basically saying nothing more than that 'Concluding' pieces feel concluded.
Essentially, I think there are pieces of music that, in addition to whatever other emotions they may convey (triumphant, pensive, etc.) also have an additional, separate quality of "conclusion". And I'm wondering what, if any specific musical constructs lie behind that quality.
Thought while watching movie credits scroll:
Are there some pieces of music more suitable than others as "closer" music? (e.g., scroll credits and that sort of thing)? If so, what is it that gives it this quality?
I mean, we all know for example that a minor key & slow tempo can make a piece "sad"; so what makes a piece feel like "aaand that's a wrap"?
This is how I originally phrased the question on Twitter & Facebook.