Note: This is basically item 3 in jkel's answer.
If you move at an appreciable fraction of the speed of light, then your shadow can appear to be "trailing" you, although it will always be "attached" to your feet if you're on flat ground.
Suppose a person is moving in the direction shown below and that there are plane waves coming in from an angle.
The left image is a top view, and the person is moving toward the right of the screen. The right image, where the person is moving into the screen, shows better the angle that the light is making relative to the horizontal.
Now think about the light rays that hit the person's head, body, and feet all at the same time, as shown in the diagram below.
The dashed lines show the path light would travel if the person weren't there. But the light does get blocked. Since light has a finite speed, it will take a longer amount of time for the shadow of the person's head to appear on the ground compared to the shadow from the person's feet.
Now all of this is for light that strikes the person at the same time. So far, so good.
Okay, by similar reasoning, the shadows on the ground at any given time are created by light striking the person at different times. That is, light that is missing and creating the shadow of a person's head must have hit the head earlier than light that is missing and creating the shadow of the person's feet. In other words, at any given instant in time, the shadow of the person's head is behind where you might expect, since that missing light struck the person's head at an earlier time.
If you put it all together, you get something like this at any instant in time:
The shadow will come out from the feet, but the head will be "behind" where you might expect it to be if the person was stationary.