Everyone that I know that has had this unfortunate problem has used some kind of tacks to fasten the linerback on. That is the only way I know to do it besides paying some one to replace the liner with a new one.
It's a very tedious job. I was able to find a link that gave somewhat detailed instructions on how to do this. A google search should find it easy enough. Be very gentile in removing the plastic uprights at the windshield and back windows as well as the piece between the front and rear doors. If it's an older car, mine is a '92, there are plastic clips attaching the uprights to the frame and they are brittle and a few broke off. Getting the headliner out of the car is tricky as well, through the back door. I had to bend it little to accomplish. I believe there is an adhesive cleaner available to clean off the old glue, I didn't use it so I have to do it over. I was able to get the headliner material on eBay for around $25. The color was grey and it was a very close match to what I have. You can get the interior adhesive from Pep Boys for $10. Make sure you cut about 1 inch extra all around. This will keep the ends from coming unattached when finished.
Get some Black MicroSuede from Ebay, a couple cans of 3M superadhesive 90, and that glue removal stuff jek1955 talked about. DIY and it will look awesome. I'm gonna do this to my headliner, rear deck, and pillars, to match my recently added black door panels, Vaders, and M3 rear seats, and my soon to be added (hopefully) black carpet, dash, and B-pillar covers.
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