Can a headliner bow be flipped without...

Much work or destroying the headliner. The headliner is perfect but one of the bows was put in upside down or it flipped

That's a weird one ! A photo might help, but:
The bows are in sleeves above where the seams are, so the risk is separating the seam or tearing the material.
Seems to me you'd have to drop the headliner back to the problem area to flip the bow.
Probably easier to work from the front than the rear.

i read the post you had in the general section about selling your hemi car, then the guy whining about stuff to get money back, including the headliner bow being upside down.
if that were truly the case, the headliner would be bagging down severely at that bow.
having installed several headliners over the years, i can't begin to imagine how this could be possible without ripping the listing sleeve from the headliner and causing damage.
this could happen during installation of the headliner, but once installed with the bows positioned as they should be, it would be real hard to do without damaging the headliner.
just my experience. your mileage will vary.

I agree.

A sleeve came apart that holds the bow, but the headliner stitching is still fine.

My headliner I installed in 1995 is separated. It looked a little low and when I pushed up on the seem I can feel a distance between the seem and bow rod that shouldn't be there. Not very visually noticeable.

But if I jerked around with it and wasn't careful maybe the bow would flip down . If you poke around like an idiot, you can find a way to screw anything up.

Truer words have never been spoken. Ask me how I know...

I wonder if the guy tried to lift the top while driving and catching air and blowing out the top, then trying move it back into place, but the bow didn’t go as planned?

iI had one that the front bow came loose after install. Not really noticeable and was that way for 30 years until I sold the car

Came loose a little ok. Flipped...absolutely no way!!!! There is no way that could happen. None

Yeah, I’m thinking it was flipped when initially installed.

I think you are right. Anyway to take down headliner without a disaster?