Continuing to discuss the views of Plato's Eleatic Stranger on sophistry, with a right turn into hardcore metaphysics with an exploration of falsity and its metaphysical correlate, non-being.
The "Eleatic" in "Eleatic Stranger" is supposed to connote Parmenides, a Presocratic philosopher who famously claimed that all existence is really One, with no real change. This means that all the variation among the things we see is really illusion: all is Being, and there can be no real thing as a lack of Being. Among the many paradoxes for language coming out of this view is that we can't even rationally say that "non-being does not exist," because in doing so we're using "non-being" as the subject of the sentence—i.e., as an object, i.e., as something that in some sense exists and has this property of not existing. And this property of "not existing" of course means "partakes of non-being." So, saying that unicorns don't exist is a matter of attributing this paradoxical property to these non-things.
If Plato/the Stranger wants to claim that the sophist is a liar, then he has to make sense contra Parmenides of the idea that a sentence can be false, i.e., can refer to a state of affairs that IS NOT, that lacks being. Non-being has to in some sense be a real thing. The eventual solution in this difficult dialogue is that the concept of "other" makes talking about non-being make sense. A unicorn is not really a non-thing; it's just a thing that's different than any of the things that are in the world, or a better way of putting it is that the situation of there existing a unicorn is other than any of the situations that hold. Falsity just means "other than truth."