We have found on the Dodge trucks from the early 90's, that the headliner material falls away from the foam instead of the foam itself desentegrating. Usually it's the other way around, the foam comes apart, but whatever the case, the foam should be removed. The 96 Dodge headliner is made of strong fiber, it would be more efficient to use a wire bristled brush to remove the foam. We have used a drill equipped with a round wire bristled metal polishing bit - that will get it pretty quick without all the elbow grease.
Below is a picture of cleaning a headliner board for a jeep cherokee - we used a soft bristled brush for this one, but that won't get the old foam off the Dodge truck headliner.


Replacement headliner kit for the 96 Dodge extended cab truck.