In my Mazda CX5 the headliner feels similar to corrugated cardboard. It has become dirty due to children, so I was wondering what the best way to attempt to clean the headliner w/o damaging it and/or having it become detached?
Spot test with some oil similar to (or exactly) Turpentine. (Not the cheap Mineral Turps, the expensive tree extract... Balsam Turperntine for example). Failing turps, use Tea Tree Oil or Eucalyptus Oil - we used to use it (Euc. Oil) when detailing as it would rub ALL the dirt off easily from Vinyl, leather, plastics. And you can really wet the area to get the dirt out of the tiny 'holes' in some parts around door handles etc. Wash off excess with soapy damp cloth, then wipe clean with damp clean cloth. (ie try not to leave much oil behind)
But please SPOT test as the material in your ceiling may corrode, bleach or stain - hard to say from here.