Usually either by being seen at a distance while oddly dressed (cryptid/ghost); or by helping out in an emergency and then leaving the scene without having been asked their name (angel.)

The former makes more sense to me as a real phenomenon than the latter. I've been helped by strangers with no identifying information and never entertained the prospect that they were angels as in some Hollywood film blanc. I have occasionally been the stranger who helps out. I would be very surprised if anyone thought I was actually the Man with No Name.

Do you have any idea why this pattern is so popular?