Headliner

The headliner of my 99 z71 extended cab is coming down around the door molding on both sides. Does anyone know if the sides are supposed to be held in by the weaherstipping? or is it a molded piece that is just coming undone at the sides? The fabric and foam are showing from the side when I open up either door and I can push them back up by hand but they won't stay. I don't know if I should take it out and see if it's glued to a molded piece underneath or what. Any suggestions? Thanks in advance.

it should be under the rubber stripping.