Good question.

According to Yogananda, there's a level beyond the auric dimension (ideation/causal dimension) and the one beyond that is the unadorned soul.
I think he defines the soul as whatever identity it happens to be adopting at the moment and that includes the physical body.
At one point in Autobiography of a Yogi, his guru descends two levels ie manifests an aura and a physical body in order to explain reality to him -- an extraordinary passage.

Anyway to answer your question, all but one of the souls I've been aware of has an aura. Even God had an aura, tho I think he adorned Him/Herself with it for my benefit.
The one that doesn't is my long-term attacker.

Crystals have an aura and a very basic soul I believe. I could be wrong on that and there might be a dividing line where a certain level of evolution suddenly gains a soul.