My foam core headliner is seperating from it’s backing. What glue would be appropriate to re-secure it?

 

Safety pins. I never really notice them when driving and my mechanic only noticed them after 3 years of having them. Glue doesn't really work because the foam has already degrading so you will be trying to glue disintegrating foam to disintegrating foam. You can buy a new headliner on Ebay.

Edit: I did see these when looking for headliners which might actually look really cool. https://www.ebay.co.uk/itm/393235382...%7CModel%3AXK8

 

FWIW.
3M. 777 contrary to what some say,, states specifically on the can that it is NOT for headliners. ( ask me how I know). 3M does make an adhesive for headliners.
I do like the safety pins in a pinch.

 

I re-covered mine. I used this foam-backed fabric (order the swatch sample for colour match) and then removed the trim pieces, sanded off all the old remnants and used gorilla glue spray to attach the new fabric. Looks good as new and no signs of letting go 1 year later.Its not the glue breaking down the causes these to separate - its the foam backing disintegrating.