Why would somebody care about the properties of things that do not exist?

Can you be more specific? There are few more or less trivial answers -- e.g. a model of some real process does not exist (it's just a model in my head) but I'm interested in its properties because the model is useful for, say, forecasting reality. Or, for another example, I might be imagining a thing that I will build and, again, the reason to be interested in its properties is obvious.