"Well, I'm quite sure that whatever I dreamt about was of paramount importance," I sighed. Then, rather than despairing over the lost opportunity, I shrugged my shoulders and rolled my eyes. "Well, there is no point despairing over it. If I can't remember it, no amount of mental struggle will change it," I decided out loud.
One could either remember their dream or not. There was no in-between as human memory would work differently when asleep than how it would act when awake.
During one's conscious period, one would store things in their temporary memory before allowing their instincts to sort all the memories and extract those valuable enough to keep them in the long-term memory.
When it came to dreaming, though, unless one practices certain techniques to reclaim their consciousness even while asleep… Then everything about the dream would be stored within the short-term memory.