Bug Linear fog and Unlit shaders

Hello!
I've recently come across an issue using the Linear fog with unlit shaders.
(It doesn't happen with the standard shader and I also noticed the issue with the PS1 shaders from the Asset Store but this time also with "unlit" disabled)

The fog seems to simply stay in place until a wall is close enough from the camera.
I tried using my textures as emission maps on the standard shader (which worked) but in my project I use the built-in unlit and custom shaders.

Here is an example of the issue in a corridor :