Headliners can be finicky to clean.
As a rule, they are fabric, glued to a thin piece of wood, attached to the roof.
Many (if not all) All Purpose Cleaners (APC) can/will cause to glue to come loose.
Another thing "Not to do" is using a steamer to clean the headliner as the fabric will fall.
You know the look where pockets of headliner fabric are dropping in many headliner areas.
You could try this tip...Use a Mr. Clean Magic Eraser (in an inconspicuous spot) to test.
Let me know your results.
BTW - Many "modern" headliners are a single piece of plastic molded to look like fabric.
Adams Carpet and Upholstery Cleaner hands down the best cleaner I have used. Spray it on a clean microfiber towel and wipe over the area, or spray entire headliner and wipe down depending how dirty it is