There are four types of existence or possible knowledge categorized. The known, the knowable, the unknown, and the unknowable. All of these are real. Beyond them is the non-existent. So even if something is unknowable, like the highest possible number, that does not mean it does not exist. It is conceptually possible even if not probable or provable.
To not exist is to not even be capable of being possible. Things we simply can't imagine because they violate not just physical law and nature, but the principles of logic by which we are capable of knowing anything. They lie outside our ability to conceive.
Existence and reality are not the same thing exactly. If existence was a container (the universe), reality would be the form and shape of the container. You can have various existences--bottle, bowl, cup. But each of those existences has a separate reality--form, condition, function.
All contents of the container conform to its existence in that the container holds them. But not everything in the container will conform to reality. If real objects are objects that take up space in the container, unreal objects are the space between the contents. They seem to have form but are actually reliant on real objects for that form. They are already unreal, but without real objects they cease to exist altogether.
For example, the mind may be real, but the mind loans form to unreal concepts such as our hallucinations. Hallucinations are only real as they exist as chemical reactions in the brain. But they are not real in they represent actual substance.