Violent or anti-social music lyrics may provide a short-term catharsis for depression and feelings of alienation, by giving the listener the company that mysery is said to crave.
In larger doses, however, the negative emotions expressed in those songs are apt to work at ingraining the attitudes they portray in their lyrics into the minds of their listeners, thus reinforcing the feelings of depression and sometimes by validating thoughts of violence or suicide. (Shneidman and Farberow, 1994)
Sometimes, when addiction to heavy metal or rap music becomes extreme, a "media delinquency" can develop, when the music becomes an actual contributory factor in a person's thoughts, decision-making and behavior. (Pezdek & Roe, 1995)
Finally, Goleman states (1995):
To immerse oneself in angry, desperate, depressing music is a poor strategy for coping with anger, despair, and depression. Neuroscience suggests that
'brooding,' or dwelling on one’s current emotional state, is more likely to
deepen the state rather than to alleviate it.
On a brief personal note, I can tell you from first-hand experience how a person's choice of music can backfire on them. My husband (now ex-) has always listened to heavy metal head-banger stuff since I've known him. When we were 20, it was not such a big deal, I guess. But as the years passed, it was like the pissed off teen rebel "I hate my parents and I'll do what I want" theme somehow stunted his emotional growth. I have long believed that the 4 to upward of 10 hours each day he has spent listening to angry, depressing anti-social lyrics as though they were a personal anthem has seriously affected his brain and the way he thinks and views himself and the rest of the world. "Hate Rock," I always called it.
So to answer the question: Yes, listening to sad music while a person is feeling sad themselves can be cathartic and is a matter of personal choice of whether to deal with their feelings that way. BUT, beware the negative effects of over-indulgence, especially in those prone to addictive behavior. (Pezdek & Roe, 1995)