Depends, this is more common with pop music. The goal as a writer is to make a melody easy to remember for the listener. Now to answer your question, my music teacher told me our brains are wired to “complete cycles” or fix problems. For ex: When you see two eggs and a sauce shaped as a “U” in a plate, it might look like a face but it’s not. Your brain makes you think it’s a face. Same thing with “missing notes” your brain tries to “resolve” theses notes (something you learn in music theory) and that’s how it’s easy for listeners to know what’s next. Most of pop music out there is made using the same harmonic progressions, that’s why you only need a couple of chords when you learn guitar to learn a lot of songs. Jazz in the other hand is another story… it’s unpredictable (which is what makes it interesting) and takes years of study.
I’m not sure but this is what I have think happens: the brain loves patterns, it tries to see patterns everywhere. That’s what makes a song catchy. Even in chaos our brain tries to see patterns and images, eg in clouds. So the missing parts of songs and music that our brain fills in is just the brain trying to fill the “pattern” that it see fit so the music is complete.
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