If you are dealing with a popcorn ceiling finish, check to see if it contains asbestos before repairing damage using this process.
A peeling or flaking drywall texture is usually due to water damage. When a wall or ceiling gets very wet the bond between the texture and the drywall can be ruined. In some cases the extend of the damage may be a brown stain that can be touched up with paint in the worst cases the wallboard is warping and requires replacement. To repair minor damage to drywall texture, use the following process.
To repair a loose, bubbling or peeling drywall texture, all the loose material should be scraped off with a putty knife or similar tool.
Around the edge of the damage, scrape back a couple inches to undamaged texture. When the finish becomes difficult to remove, stop scraping. Try to leave a clean edge to make blending the new texturing easier.
Remove the dust and prime the whole area with primer–sealer. If the damage is due to water, it must be sealed with a primer or the repair may not hold. At the very least, the stain will bleed through the finish if not primed.
If you are going to repaint, you can overlap the edges with the primer. If you're not painting, keep the primer off the surrounding textured finish.
Restore the textured finish working from the center out. Use light pressure at the edges to blend the new texture with the old. See Matching a Drywall Texture for help with simulating an existing drywall textured finish.