It seems to me that the ideas explored in this discussion of DN11 echo those we discussed earlier about the meaning of AN4.173 viz. “Is there something else beyond the 6 senses?”. They also tie in neatly with the fire simile in MN72. The failure of the Buddha’s contemporaries to grasp just what he was talking about can be attributed to their sakkayaditthi - the insistence that “Some Thing must Exist!”
When a fire runs out of fuel, it ceases. Another way of stating this would be to say that when the fire runs out of fuel, it no longer appears. That does not mean that the Fire now Exists unseen on another plane / in another dimension - that would be Eternalism. The fire doesn’t ‘go’ anywhere - it just goes out. Yet, at the same time - that does not mean its annihilated. Fire is a Process, without any Permanent Substance - it cannot die because it was never born.
Similarly, Mind and Consciousness are simply dependently originated natural phenomena - empty of any permanent, enduring, exclusively satisfactory controllable Essence (Self).
They are impermanent (AN10.60) and should be abandoned… but that is hard to do as they are the last bastion of the conceit of Self (SN12.61).