UPDATE: see posts below starting with #8 for some remarks and points of recommendation on reupholstering of the headliner, with photos of the process and completed job. Hopefully I will have been able to offer some helpful incite, original spin, and additional perspective in the same way posts by others were helpful to me.
( I'm now less aggravated than my first post here - below - especially with the finished work coming out as nicely as it did.)
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I have looked through several of the headliner sagging/removal/repair threads, and this is not my first time in going about it, considering I have had numerous cars through the past 40 years that were afflicted with this virus. With that in mind...
I'm just here to rant.
This issue has been going on since at least the first flimsy foam-backed polyester headliners fitted in cars of the 1970s. Why after 35 years could they still not get this right? I went out to my SRT-6 today to find the passenger side sagging down like a giant elephant nut-sack.
My car only has 32,000 on the ticker, is NEVER stored in the hot sun, always parked in a cool garage, or under a full-length canopy even when it is outside - NEVER parked or driven in the rain - EVER. I never drive it with the passenger window down except at suburban street speeds, and this didn't happen while driving the car last time. It happened at some time during the past week - just sitting doing nothing. The climate these past three months has not had one single hot day that would be an expected as a condition to cause this, so that wasn't it. Last hot day it was out was probably last October.
I think of all the cars I've had the aggravation with this BS through-out the years, I can't believe I now have to tackle this crap again, on what is a like-new car from as late as 2005.The embedded photo was taken last Thanksgiving weekend 2019.
Just a SHORT list of the cars I've had to tackle with this problem throughout the years; geographic location/climate not a factor as I've owned the cars of this list on the East Coast, the Midwest, and the Crossfire here in mild-mannered California, most all were garaged majority of the time. I hate to say it but I've never seen this problem arise in any Datsun, Toyota, or Honda. I've had 3 different 1st-Generation Datsun 240Z and a 280z, and a 2nd Generation 280zx, then later a 300Z - never happened. Sister's 1980's Celica - never. Parents 3 different Camry's - never, girlfriend's 1996 Toyota Pickup, then later a 2003 Solara - never.
1973 AMC Javelin SST
1974 AMC Javelin
1981 Buick Regal-T Type
1980 Pontiac Sunbird
1985 Merkur XR4ti
1985 Cadillac Eldorado
1985 BMW 525i
1986 Jaguar XJS
1988 Merkur XR4ti
1989 Ford Mustang GT
1990 Jaguar XJS
2005 Chrysler Crossfire SRT-6!! 
I've got 3 other cars from the 1960s that I've owned for 35 years, 25 years, and 16 years respectively - and NOTHING ever simply falls apart, off, or sags on them just by sitting parked in a garage.
OK, I'm done. I know it's a simple job, but manufacturers should have been able to get this issue permanently solved by now. They have the polymers, epoxies, and seals to do it that should last a millennia without needing repair.
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