The burning of a fire produces flames, it is dependent on fuel & supportive conditions, burning is conditioned. The extinguishment of flames depends on the exhaustion of fuel and requisite conditions for burning. We can say that the cessation is conditioned by the process of burning and exhaustion of fuel.
However extinguishment is not a thing among things there; it is not the fuel, it is not the flame, it isn't the perception of burning, it is not the heat.
It is like the end of a story, there are events leading up to it but the end in and of itself is not part of the narrative, it is not something that is experienced by a character in the story, it is not an event occuring for this or that personage and like extinguishment is not a thing among the things that are extinguished or said to end.
Therefore when we talk about the principal extinguishment of the conditioned, the extinguishment principal is then by definition unconditioned because it is not a thing among the conditioned things that are there extinguished.
The cessation of a flame is a truth to be observed & known as the non-occurence of burning. The cessation of the conditioned is a truth to be observed & known as the non-occurence of the conditioned or that which changes as it persists.
Just like the extinguishment of a flame is not a thing among the things that are said to be extinguished, so is the extinguishment principle of the conditioned is not among the conditioned things.
The name of a person is neither his mind nor his body, here analogically the semantics of our understanding are such that name of a thing is not found among the things that are named.