Lets call this a hypothetical question, as there is no way I would ever underdevelop a roll of film.
My thought was that film that has never been in developer is opaque. Pull a couple of inches of35 mm out of the canister. You cannot see through it. Unexposed film that has been in developer just the right amount of time is almost transparent. Never having been good at math or physics, I would conclude that on unexposed film, density decreases with development.
Unexposed parts of the film (after development and fixation) will have an opacity equal to b + f, and this (almost) regardless of development time. I guess if the development time was extremely short, the fog density could be lower. (Has anyone measured the b + f of unexposed and fully fixed film?) b + f would certainly not increase with under-development, I think
fog only shows with development so the density of a undeveloped, fixed film would be equal to B. The F would decrease slightly with less development.
Density always increases with development because halide crystals are being converted to silver, which is what we see in the end. Fixing reduces the density of film. When you pull film out of the canister, it slowly turns black because a massive amount of exposure converts a little halide into silver, similar to a little bit of development. Development does not reduce density of unexposed film no more than painting a white house with no black makes it more white.