As the previous poster has pointed out, if it is foam backed and the foam is disinegrating, it's toast. You can test this in a firm part of the headliner like a corner. If you press in and the foam does not spring back, it's only a matter of time before it comes down. Do not, under any circumstances, replace it with another foam backed product. It too will eventually fail. This type of material used to be common in cars of the 80s. I made a good living replacing them in the 90s.
There are other choices that are better such as stretchform. That is the fabric
on the floors and sidewalls of those cars. Cheap
, hides well, conforms to humps very well, easy to install.