Does the deep subconscious dream during the sleep interval, or is it active and on duty round the clock?

The deep subconscious, like the upper subconscious, is always awake and always thinking and aware of things. So it continues to ruminate, conjecture, review, survey, and explore via its own thoughts, especially during the dream interval, as it need not keep one eye on what the conscious level of the mind is doing. It is largely existing and living on its own because the upper reaches of the mind are unaware of its existence and do not communicate with it directly.