The headlining is foam backed material. The foam deteriorates with age, more rapidly if its exposed to high levels of heat. As the foam deteriorates and turns to powder, it leaves some foam on the back of the material and some on the cardboard backing. Just using glue won't solve the problem as the material won't bond well with all that old foam in there. Plus it will still look bad and won't stop the problem from getting worse.
I highly recommend removing the whole backing board out of the car, clean it well and replace the material with new foam backed material available from an auto upholstery supplier.
_A_D_A_M_ posted a good link to the "how-to" section. Have a look at it, it'll make you realise that its easy enough to do.