I've taken a couple apart in junkyards to get a closer look. I don't believe the headliner is attached to the rear portion of the roof using glue.

It appears that the bow is inserted into a pocket sewn along the width of the headliner. The ends of the bow fit into rubber grommets near the top of the C pillar. The grommets deteriorate and allow the end of the bow to slip into the C pillar area allowing the bow to straighten out and sag. Normally the bow is held in tension by the grommets up against the top of the roofline.

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