Sentence without a main clause?

What do you call a phrase without a main clause? For example, answering a question:

Are you to blame for the increase in deaths?

Of course not!

The answer cannot stand alone. Is there a name for this?

Edit: Above is not a good example.
I am trying to explain spoken language as a written text. The text is an interview. The interviewer has asked a question, and the answer starts with 'because' and refers to information in the question, and alone does not make sense. So it cannot stand alone. Does this make this a sentence fragment/subordinate clause or something else?