Yup agree 100% the foam is deteriorated and is crumbling apart. 3M makes a headliner spray, but in thi case you need to remove the headliner, remove the fabric, then clean all the gunk of the headliner, reapply the foam and re gule the fabric. I had my GTO headliner redoe for about $125 plus the fabric which I found on headliners4cars.comIt is likely to not stick. The reason it is falling is because the foam underlayment is failing, turning into a goo. Any glue you put on there will bleed right through the material and probably not stick to the backside. The flipside to that is, you do not want to just pull that off and leave it bare. You'll regret it. The only real fix is to pull it, strip it, and do new material.
Honda USED to use that type of vinyl headliners in older model Accords from the early 2000s and prior, they lasted forever.In the even that I just go ahead and get the headliner replaced, I have a question. My 300ZX's headliner is what I'm guessing is "pleather", to match the leather interior. A 25 year old car and it's still in showroom new condition. Can one like that be installed in my Accord instead of that cheapy thin fabric crap? My Accord has leather interior as well.