Consciousness is often said to disappear in deep, dreamless sleep. We argue that this assumption is oversimplified. Unless dreamless sleep is defined as unconscious from the outset there are good empirical and theoretical reasons for saying that a range of different types of sleep experience, some of which are distinct from dreaming, can occur in all stages of sleep.
See for me I'm not sure why that's hard to accept. I think I first heard it from Alan Watts, that there were billions of years of space before I was conscious, so why am I afraid of billions of years of nothing after I'm gone?