Bear in mind that fiberboard doesn't stand up to moisture very well. It's a lot like thick cardboard.
So I pulled the damaged sheet off. Or rather, I started to. Because of the water damage, the nails that were holding it on-- or were supposed to be holding it on-- had pretty much rusted out of existence, so an entire 4 x 8 foot piece came down along with all of the old cellulose insulation and about five pounds of dust.
Yes, I am wearing a dust mask.
I'm putting some extruded polystyrene (pink foam board) in to replace the old cellulose. I happened to have some on hand.
What kills me is that this was another "fix" of the previous owner, who not only failed to fix the leaky roof, he shoved broken pieces of fiberboard up into the space where the insulation was supposed to be... I don't really know why. I suspect it may have been an attempt to hide the leak or something. He also used an old picture of the first owner of the house to screw into the wall to replace a damaged piece of the fiberboard.
When the hardware store opens, I'm going to get more spray foam to help seal some other leaks.