"He listens to" by itself is not a complete thought and cannot function as an independent clause. However it is a complete thought when used in:
- "The music he listens to." (Used in casual conversation as a reply.)
- "He listens to crappy music." (Proper sentence that is correct when 'he' is defined, which in this case we will say is. This use is different than the first.)
I don't like the music he listens to.
This is a full sentence. The subject is I, the verb is the phrase "don't like", and the noun being modified by the subject and verb is the phrase "the music he listens to." If you say "...the music.", you must have "the music" predefined to use it, so it relies on more detail which "he listens to" provides. "He listens to" does rely on more information but not in the way you may think, which depends on usage. "The music he listens to" is a full nominal phrase, so you treat it as a noun. It's used differently in the sentence "He listens to crappy music" where the subject is 'he', the verbal phrase is 'listens to', and the noun is 'music' which is modified by the adjective 'crappy'.
- The music - is a nominal phrase that requires predefinition.
- The music he listens to - is a nominal phrase that defines itself.
- ...he listens to - is a relative clause, though if you wanted to be technical about it it could work better if you added 'that', as in "...that he listens to." In this case, if you think about it, it's like a weird adjective. (What don't you like? The music. What's wrong with the music? It's the kind that he listens to. What looks ugly? The color yellow. What's wrong with yellow? It looks gross.) It is a relative clause.
"The work" is similar to "the music", it requires predefinition for use if you're going to use it by itself. If you're going to use it and self define it, that turns it into a nominal phrase that defines itself.
The work he did was boring.
To use this you'd need to predefine who 'he' is. Compare this to:
The work my brother did was boring.
You could also say:
The work in Manchester was boring.
So obviously "he did in Manchester" isn't necessary as long as "the work" is predefined somehow.
Think of it this way, if you randomly went up to someone and said "The music/the work is terrible!", aside from the strange look you'll get for being a stranger, they would ask "what music/work?" If you went up and said "I don't like the music my brother listens to!" or "The work my brother did in Manchester was boring!", they would respond with an "I don't care about your music choices or lack of entertaining work, I hardly know you!"