If you get such a result in manual operation of your calculator, you may frown but usually know immediately what you did wrong. If, OTOH, such a result is returned by a routine, it may cost you some time and effort to find its origin - then you will try avoiding this "error" case in future by applying suitable means.
Now the question: Will you ever throw such a NaN result into a subsequent calculation?
I.e. put something non-numeric into a numeric procedure?

Of course you can, and I've seen some academic examples where this was done - but does anyone know a real-world problem where this turned out advantegeous or beneficial? (No computer science but down to earth, please.)
Thanks in advance for your answers!