The fiber board was most likely installed to conceal some irregularities with the plywood or particle board below it. If the fiberboard itself became unleveled, there's really no reason to keep it there. You may have to strip and level the floor below it using a combination of additional screws to hold down parts that spring out too much, sander to sand off parts that cannot be held down by the screws and floor leveling compounds for anything that could not be treated by screws and material removal.
Alternatively, you may be able to take a closer look at the fiberboard to determine if you can apply pretty much the same techniques to it. See if you can screw down some of the most sticking out pieces. How bad is the de-lamination, could the separated layers be held down by the weight of the floor above it?
Also, keep in mind that you'll be using soft underlayment with any laminate or floating engineering wood floor. The foam underlayment is about 1/8" - 3/32" thick and can actually cover some of the smaller imperfections. In other words, the fiberboard doesn't have to have a mirror-like surface, some of the minor surface issues can be disregarded because they will be taken care of by the underlayment. Â