The texture applied to the back sidedef of a linedef that has a "lower unpegged" flag moves with the sector. Usually it doesn't matter because it is used for doors, and doors usually do not have a visible back sidedef, but there are exceptions:
Several maps in Heretic have kind of bars that go into depressions in the ground, so that your path is blocked, then these bars can be raised, opening the path. So the front sidedefs delimiting these sectors have the texture of bars, while their back sidedefs have the texture of the sides of the depressions in the ground into which these bars are plunged in their original state. So when you raise the bars and look at the depressions, you see that the textures of their sides are moving up.
This can be observed, for example, in the very beginning of Heretic E3M1, and some other maps.
I can make an example map if needed, I just thought that it's more reliable to give a Raven-created map, so that it's clear that it's not something that I messed up.