The headliner boards in the Jeep Cherokee's are made of fiberglass with a thin film of plastic laminated over it. They are rigid enough to hold the headliner in place and provide insulating qualities, however they are quite "delicate", but remember, the headliner holds nothing up, just itself. There is really no good way to repair it once it comes apart.

The best way to apply the headliner material back on the board that some of the layers of fiberglass have come up is...
1. spray glue over the place and let it dry, just to keep it from flaking any more (the glue will soak in somewhat and give it some consistency there)
2.if it is a smaller spot, let the material float over it (stretch the material a little tighter over the spot, and don't glue it there). If done properly, the job should last for years without the need to repair it again.
To see a jeep cherokee installaton, click on this link.

This headliner kit will fit a Jeep Cherokee, all year models.