The Saturn headliner is a fiber based board to which foam back fabric is attached. The fabric is typically glued onto the fiber board. Over time and due to exposure to heat, etc., the foam deteriorates and the glue releases.
To do it right, you need to take the headliner out of the car, remove the old foam/fabric, and glue on new foam/fabric. One thing you might run into is the plastic clips and such holding it all together in the car may be brittle from age. You are likely to break some removing the headliner. If you really want to do this, you might look for a shop that does that type of thing (they are out there). The money you spend getting it done will likely be less that you spend on parts and materials, and will certainly be worth the hassle of doing it yourself. Use the time for more enjoyable activities.
Time to get that Miata.
