Asankhata is described as ‘what has no characteristic to arise, cease and change’.
It was this what the Buddha sought, after realising that nothing that has the opposite features (sankhata) is reliable. For me this is also the meaning of: all that is liable to arise, is also liable to cease. There is just no safety, protection, refuge in such. The whole domain of the conditioned cannot fulfill our heartwish for the end of suffering because it is all fundamentally not stable, unreliable.
It will always desintegrate some time, sooner or later.
Many sutta’s make perfectly clear that Buddha sought what is reliable, in other words: that what is stable, constant, not-desintegrating. Because, anything else cannot really be a refuge, safety, protect.
I believe it is universal that we all seek what is constant, reliable, what can protect in this unsafe world.
Buddha brings this light in the world, that this is not a hopeless mission to seek for the stable, constant, not desintegrating. He teaches he found it. He called it asankhata, Nibbana. It is not affected by arising, ceasing, decaying, change, aging, the unailing, the deathless. That is what he found and in that his search came to an end. His heart was now at ease. Not at ease with the prospect to finally cease at a last death, but at ease because his heartwish to find the stable, the not-desintegrating was fulfilled.
I believe, people come to the wrong conclusion that seeing asankhata as real, seeing Nibbana as real, is the same as introducing eternalism and self in Dhamma. This is not the case. One cannot talk about asankhata as something that eternally exist. And seeing it as atta, a kind of personal core, eternal entity-like, is surely not appropriate.
So, back to your citation: i believe we can very well think of parinibbana without a self and still also as not a mere cessation. It just says that there is more to life then khandha’s. There is also Nibbana.
Asankhata , i feel, transcends all such designations as exist, truly exist etc. So, i also do not think this line of reasoning brings us anything closer to realising Nibbana.