Hi Brian,

You're talking about the headliner.  It is material that is glued to foam
backing which is then glued to a cardboard form that is attached to your
car's roof.

What happens is that after it ages the foam rubber backing deteriorates and
pulls apart.  The best thing to do is to just replace the entire headliner,
material, foam and cardboard.  You can try gluing it back together but the
foam will continue to deteriorate.  It probably won't last for long because
you're trying to glue the half of the foam attached to the material to the
other half that's attached to the cardboard.  The glue didn't fail, the foam
just fell apart.  Since it's deteriorating anyway it probably wouldn't last
very long if you tried to fix it.

You can get a replacement headliner at almost any auto interior shop but it
probably won't be the same type of material the factory used.  If you want
to maintain the original factory material, you can try buying a headliner
from www.classicindustries.com or any of the other restoration suppliers.
Take it to the headliner shop or try installing it yourself.  It depends on
how handy you are.

I hope this helps.

David
'67 RS/SS Camaro