Underlying assumption of consciousness is that one must be first conscious of himself. Cogito, ergo sum and other similar stuff. This is not a hard definition, or set in stone. Yet, practically all philosophical schools or religious traditions, implicitly if not explicitly, assume that one must be present, aware of himself and his mindstream before reflecting on anything else.
Parallel to this, definition of unconsciousness is simply of a state where person is not being aware of himself, therefore not being aware of his surroundings either. Again, this is not a strict philosophical definition, but it is used for example in medicine or in legal matters.
Now we come to the main question, being conscious of nothing. We must assume that person being conscious of nothing is still conscious (otherwise he would be simply unconscious ) . Therefore, he is aware of himself and he does exist in Cartesian sense. But, other than that, he experiences nothingness. This could be part of meditation, or Brain in a vat scenario with every empirical source of data (every sense) being cut off. But such person would still retain sense of I am, I exist here and now (even if I don't know where and when this exactly is) . He would also retain ability to reflect on ideas already existing in his mind . This is fundamental difference between him and someone who is unconscious, not being aware of himself, therefore not being able to track his own mindstream, therefore not being able to reflect.
There is also interesting question about lucid dreams where dreamer has certain degree of awareness, but not on the same level as in woke state. This is borderline state between consciousness an unconsciousness with "false" empirical data coming from the senses (if we assume that world in a dream is not real) . Therefore, if a dreamer knows he is dreaming, then he is aware of illusion, therefore at least partially aware of nothingness.
