I'm wondering if it makes sense to talk about worlds which aren't this one being real.
It seems like you can claim that something possibly exists.
Now I'm wondering, because it seems to amount to the above question, whether I can claim that it is possible for something to exist, but it actually doesn't, and in some other sense actually does.
When talking about possible worlds, "actual" is used to refer to this world, i.e. the one we live in. Thus you can say "I could have been president, but actually I am not". In possible worlds words, "there is some possible world in which I am president, but not in this one."
In direct response to your question, keeping the terminology in mind, one can say: "there actually aren't any unicorns, but there could have been", thus using the existential quantifier with a modal operator. The sentence "there could have been unicorns" is formalized as follows:
◇∃xUnicorn(x)
Read "It is possible that there are unicorns".
This may sound odd, and indeed some have objected to introducing quantification to modal logic (the logic that deals with possible worlds), most famously Quine.
It is of course important to be clear about what kind of possibility you are talking about. For example, some things are logically possible, but not physically possible. It is logically possible for me to jump 100 meters in the air, but it is physically impossible. Physical possibility is usually taken to be as in accordance with the laws of nature.
So, you may say that it is logically possible that there are unicorns, but physically impossible (say in case they have some property that is incompatible with the laws of nature). You have to specify the kind of possibility you are talking about to avoid equivocation.
