Are there any reputable philosophical works that talk about the fear of non-existence as opposed to the fear of death? (Of course no one can imagine what it 'feels like' to not exist but if many people have a strong desire or drive to 'keep existing' in a manner to which they are used to they will fear anything that could stop them in their tracks and wipe out their existence forever.)
To give an immediate answer, yes philosophers have traversed the subject. Epicurus was the first to pose the challenge of non existence after death, Thomas nagel more recently discussed the subject, that's a good place to start.
It might be possible to argue that Roquentin, in Sartres Nausee, when faced with the pure facticity of his surroundings experiences angst and unease; the nothingness of matter without mind, is that it lacks subject hood; and our his subjecthood not being affirmed, fragments.
This is not quite non-existence, for the surroundings surely exist for Roquentin in their very material haeccitas (thisness); and not is Roquentin being faced with a sense of his mortality; but that he is not kin to a rock, or a table or tree.
Many would argue, including Freud, that the concepts of after life and eternal soul were invented as a response to fear of non existence. People were so traumatized by the idea of non-existence after death, that they invented religion and mythology as a coping mechanism.