Art by smbc-comics
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.
Pubmed Articles
Does Consciousness Disappear in Dreamless Sleep?
Sciencealert Article We Were Wrong About Consciousness Disappearing in Dreamless Sleep, Say Scientists
I think this is false but I don't have information to refute it other than my own experience. I used to write a dream diary. When I did, I remembered my dreams almost every time I woke up. Not just half the time or 80% but more like 96% of the time. And it was very detailed with multiple dreams tied to each other.
I kept a dream journal for a couple of years.
Subjectively there was no way for me to know if it was memory or just my tired brain making a story out of the left over bits of sleep.
It did fuel a lot of creative writing though (both in and out of the journal). And helped me be more in touch with my emotions.
I remember I've had dreams but I only have a very vague sense of what they are about.
It's not false. I remember my dreams every morning, and often remember them for a long time. I also have sleep issues and never get restful sleep.
There's naturally far more nuanced to the neuroscience, but it's largely true.