The context for this is the diagram from From where (in space-time) does Hawking radiation originate? - the more I think of it, the less it makes any sense )
This particular question is about vertical line on the left of "after evaporating" zone. What would prevent the light from crossing it? As the light travels diagonally, it must be able to cross it towards up left, but where to? Also, if there is something, the light must be able to cross back into normal space (top right direction).
Both vertical lines in this diagram, i.e. one "after" the evaporation as well as the vertical line in the left lower corner (and all vertical lines without "teeth" in all Penrose diagrams in the world) describe the vicinity of the point $r=0$ in polar coordinates. One can't "cross" these lines because there are no points with the radial coordinate $r\lt 0$.
An observer moving along the vicinity of the lines is simply moving near a regular point of the smooth spacetime, $r=0$ or $(x,y,z)=(0,0,0)$, and if such an observer moves through the very point $(0,0,0)$, he reappears on the opposite side where $r$ is positive again. Using the diagram, he bounces off of the vertical line.
The Penrose diagram neglects the spherical angular coordinates $\theta,\phi$ because the whole geometry is $SO(3)$ rotationally symmetric – i.e. invariant under these rotations. That's why we don't lose any information about the geometry by ignoring the angular coordinates. However, particular point-like or localized observers have particular values of $\theta,\phi$, and these values are not shown by the diagram.
