In close listening to the counterpoint of, say, Bach, we imagine voices continuing even after they have died away because of the logic of the voice-leading--in that sense the listener 'completes' the music. Sometimes you can only 'hear' the full texture by looking at the score! But the Romantics went further. In one part of his Humoresque, op 20, Schumann writes a separate melody on a third stave that is meant to be unplayed!
The top stave is the right hand, the bottom stave is the left hand and the middle is, unheard, inaudible, to be imagined. He writes in the score, "inner voice", in the sense of 'interior'. Here is a bit of the score:
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The written out top voice is a kind of echo of the 'interior' voice, which is not played. Here is a performance by Horowitz. The "Hastig" section starts right at 5:55:
Now I know what you are going to say: "But I don't hear that inner voice!" Well, yes. Thinking about this can get a bit tricky. Here we have an unplayed melody that is presumably thought or imagined by the pianist while he is playing that perhaps influences the way he plays and thereby the way we hear it. But we are really free to hear music any way we want to. Call this an experiment in Romanticism.
I have another, quite different example. Here is the Quebec group Beau Dommage performing their song "La complainte du phoque en Alaska" in concert. The audience joins in from the beginning and by the four minute mark, take over singing the song. At the 4:43 mark, the band stops completely and only comes back to end it. Nice.
UPDATE: Beau Dommage (the name means "beautiful damage") was a hugely popular rock band in Quebec in the 1970s. This clip comes from a reunion concert in 1995. A "phoque" is a seal.