Like our 2d screen is flat so you say its a plane that plane has a imaginary line that is perpendicular to it.
It would be pointing straight into or out of the screen. That is typically called the surface normal to a polygon or to a plane.
Edit pictures better.
like in the above image i posted on the bottom part of it. The vertical red polygon line is perpendicular to the direction of the blue flat polygon line.
As that blue polygon line is raised to be exactly drawn so its edge or its plane lines straight up with the forward view direction
(flat to your eye like a piece of paper edge on)
and the surface normal of the blue polygon becomes exactly perpendicular to the cameras forward.
Then the dot product calculation to any pixels normal on that plane returns zero and as shown in the upper part of the above image.
The blue line disappears cause the vertex shader clips it out.
Other wise you could rotate your whole 2d scene on the X axis 90 degrees. Move your camera to be at your player position in that plane. Render everything once view forward then view back, with the depth buffer on.The z depth would be on a Y line 1 pixel high as the entire scene would be on a ZX coordinate plane. Use whatever depth resolution you wanted in width.
Every polygon would render like you were looking at a piece paper edge on in a long line.
Take two snap shots forward back and you have a 360 degree depth buffer from the viewer.
The above depth buffer (rendered as a line were the x coordinate is thought of as a degree bering) then represents the atan2 polar coordinates of all regular scene drawn polygons when drawn in the shader (pixels - the player position) = a direction that can be used by atan2 to get a linear value to line up with the stored depth line along its x coordinates.
Compare that xy pixel to viewer distance to the coresponding x coordinate value in the depth buffer. So if its more then the depth value recorded in the rt depth buffer at
y = 1 and x = atan2(x,y) / pi (or /360) when less then 180 degrees or y =2 for the back view when more then 180 degrees.
Then it is in shadow.
Maybe later ill give this a shot, im not sure it can't be made to draw that edge or maybe it doesn't matter as long as it's not really cliped maybe the disappearing is just a math artifact.