Well. Good thing these hypothesis make different predictions :P

Existence is reserved for things we have access to. Possible existence implies possible access. Actual existence implies actual access. Non-existence implies no possible access.

It is certainly possible to describe things outside of all possible access. For example as mentioned above we can talk about "non-actual or nonexistent things" and "possible worlds" that we can't access because they are counterfactual or because they are a separate reality. But when we talk about things beyond all possible access, we are just making up stories, and we can say anything. For example: All non-existent things are blue, and they are also simultaneously non-blue.

This reshapes the question to "Can something exist even if we don't have access to it.".

Although I am tempted to say that it certainly seems possible, I believe that the best approach is not to make any claims about anything beyond our access.

The question of whether there are things that don't exist should lead us to consider the urgent question of whether there exist things that are not.

Also related are Meinong's Jungle and Noneism.