John, this is a very common problem: the headliner is foam-laminated vinyl. In time, the foam rots, releasing the vinyl. There are two tricks: first, scrape or wire-brush all the loose stuff off or it will affect the bond of the new stuff. You need not remove all traces of old adhesive, just the loose stuff. Second, use a high-temp adhesive to glue the new(or reused) headliner. Otherwise, the roof will heat up in the midsummer sun and relese the new glue, allowing your headiner to sag once again.
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