The question, “What is the state of the Arahant after death?” arises because of the subtle clinging to the idea that an Arahant has a self. But since the Arahant has no self, he does not enter into any state of eternal existence in some heavenly world or as a universal self in some impersonalized form. Also final Nibbana is not a state of annihilation, since there is no self to be annihilated or extinguished. What we call the Arahant is a dependently arisen process of becoming, and the attainment of final Nibbana is cessation of this process of becoming. To try to speak about what lies beyond the ending of this process is to venture outside the boundaries of conceptualization, outside the boundaries of language.

The Buddha says;

So from this we see that concepts cannot conceive the ‘inconceivable’ and the mind cannot measure the ‘immeasurable’.

The Buddha illustrates this with the example of a fire. Suppose there is a fire, burning in dependence on fuel, the sticks and logs. Now if the fire does not get any further fuel, when it uses up the old fuel, then it goes out. Suppose we ask, when the fire goes out; where did it go? Did it go to the North? To the South? To the East? To the West? The answer to this is that none of these questions apply. All of these are inapplicable. The fire has simply gone out.