I’ve always appreciated Ven. Thanissaro’s use of the word “Unbinding” to describe the cessation of craving. If you are a person who understands the binding of the mind, then the ontological nature of Nibbana takes on an interesting meaning as its opposite.
To be bound by “mind”; to be gripped by your own mind - is true pain. It is the clinging of consciousness to itself … and, when that same consciousness no longer has anything to cling to (in particular the sense media), you experience cessation (like the fire going out).
I think it’s worth noting that before “mentality/materiality” (in DO anyway) we have consciousness, and that the Buddha also spoke of a “mind made body”. The mind and body are closely linked by consciousness, and the ending of the mind-made body is what constitutes “cessation”.
This is what, IMO, makes Nibbana as “extinction” different than the “annihilation” of a “self” which “never existed in the first place”. There is a Self, essentially speaking. It is the “mind-made body”. But, in an other sense, since even that “mind-made body” is a construct it’s not accurate to call it a Self. Nor is it accurate to call the deconstruction of the mind-made body the Self.
It is accurate to call the deconstruction of the mind made body the “extinction” of all concepts of the Self. More essentially, the deconstruction of the mind made body is the extinction of what the Self does (eg. ties us to Samsara).
If I had to say anything about “cessationalism” vs. “Continualism” it is to think about the “Deconstructionalism” of Unbinding. It neither comes nor goes. It is just taken apart. And what is left is unconditioned. So, I submit to those reading , the term “deconstructionalism”. 
And, in this way, Thanissaro’s “Unbinding” makes deep sense. When we enter Nibbana we do so by the cessation of craving. That process eliminates consciousness. Consciousness binds the skhandas, the Self to the body, the Self to the mind made body, and the inner workings of the Self which drag us through Samsara.
Putting down the Self is like putting down the sword and walking away from the battle. And that’s my two cents € and I’ll end this with a rather long quote from a sutta which highlights the “perception” of “cessation”.
It could be, Ānanda, that a mendicant might gain a state of immersion like this. They wouldn’t perceive earth in earth, water in water, fire in fire, or air in air. And they wouldn’t perceive the dimension of infinite space in the dimension of infinite space, the dimension of infinite consciousness in the dimension of infinite consciousness, the dimension of nothingness in the dimension of nothingness, or the dimension of neither perception nor non-perception in the dimension of neither perception nor non-perception. They wouldn’t perceive this world in this world, or the other world in the other world. And they wouldn’t perceive what is seen, heard, thought, known, attained, sought, or explored by the mind. And yet they would still perceive.”
“But how could this be, sir?”
“Ānanda, it’s when a mendicant perceives: ‘This is peaceful; this is sublime—that is, the stilling of all activities, the letting go of all attachments, the ending of craving, fading away, cessation, extinguishment.’
AN11.7