Ākiñcañña is often translated as nothingness.
The dictionary says:
Ākiñcañña (nt.) [abstr. fr. akiñcana] state of having nothing, absence of (any) possessions; nothingness (the latter as philosophical).
"Nothingness", stating that nothing really exists, is nihilism, a wrong view. And as for 'state of having nothing, absence of any possessions' perhaps possessionlessness could do, however that is not quite how ākiñcañña is used in the texts, as there the context seems to be about emptying. So let's look into this.
With emptying, emptiness, a previous 'something' on the foreground was due to the lack of interest demoted where it then fell away from the present perception. A previous 'something' does thus not exist in the present perception as it was emptied of that.
This we see quite often for example as with the ardent aware meditator who would be disciplining avarice plus discontentment about the world. With the worries and concern about the world gone, the interest is gone, the world is gone. Or as with "Emptiness, concise (MN 121)" where first the men were gone, then the village, then the forest, then the earth, then endless air and so on. It is the reference to these objects which is gone what for the mediator makes the object gone.
And this not only goes for a particular 'something' but it also applies to the general 'something'. SN 40.7 shows that by drawing back from all 'somethings' the notion is 'not exists something' (natthi kiñcīti). But as perception has not ceased it must then mean it is 'without object'. So a perception has an object till, also by emptying, it is without.
If perception is, but without an object, it means that this 'without an object' itself then is what remains as base (as this is what is perceived). Next, by withdrawing from there we can't say there is no perception, withdrawing is a matter of perception, and we can't say there is perception as it went beyond any 'objects' and beyond 'without an object'. What then remains is 'neither perception nor no perception' as base.
A base is a base for touch. Thus has cognition not ceased, has touch not ceased, have feelings not ceased, has perception not ceased. So "nothingness" won't do and possesionlessness is besides the point. We can call 'without an object' objectless, then for the state we get to use objectlessness:
'... with objectlessness as base, perception of endless cognition as base has ceased; with neither perception nor no perception as base, perception of objectlessness as base has ceased ... '.
Pāḷi-English
Ākiñcañña (nt.) objectlessness.