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I'm pretty sure it's just glued on or held in with pins or something. They sell replacement ones. I can't imagine it being too hard especially if you pop the top off and get it on a bench or some sawhorses. I replaced the weatherstrip channels and rubber on my top a couple months back. Might be a good time to replace all that stuff too if you're messing with it.
Just make sure you get the correct headliner glue. It's surprisingly expensive at auto parts stores, but anything else will not hold up. Ask me how I know...
I have had ok luck with 3m super 77. The right stuff is labeled as specific heainer adhesive, 38808 or something like that. I am going to try permatex headliner adhesive when I redo my mini headliner.
Here's another headliner option to consider. I performed this technique instead of using all that adhesive to try and fix my droopy headliner: Remove the roof panel and flip upside down on a padded scratch-free surface. Get a small dry wall putty knife/spatula blade. Use the blade to "tuck" the loose headliner fabric back into/under the seams around the borders and make it taught all around. Once it's all taught the way you like it, you can apply a bead of matching silicone sealer around the entire tucked-in fabric. Mine was black, so I used black silicone. Now, the fabric will not be adhered to the interior of the roof panel with this technique, but it will appear to be even though it's stretched tight with approx a 1/2" or so gap between the fabric and roof panel. It even works while driving with both windows down, not flapping with incoming wind. I'm 6ft tall and my head still doesn't touch the headliner fabric after this repair.
Mine was loose 9 years ago. went to a local shop to question what glue. The tech said the glue must be a certain glue or it would not hold. I wrote it down and as I was leaving I asked what tey would charge to fix it. Trying to see how much I would save. He said $70.00. Took the top off and left it there. No regrets.