It's impossible to hang anything heavy from drywall without either hitting a framing stud or using a drywall anchor. Without an anchor, the wall will crumble, the screws will fall out and create a hole and the object will fall from the wall. If they're not installed correctly, however, drywall anchors may start spinning around inside the drywall, providing no security for your wall hangings. They must be removed and replaced in a different location when this happens.
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Pull Them Out
If a nonexpanding anchor head has not been pushed completely behind the drywall, it can be pulled out with the tail of a hammer or another gripping object such as tweezers. Use a utility knife to create a small gap between the anchor head and the drywall, and then you can pry the head from the wall with the blade or the flat end of a screwdriver or putty knife.
Push Them In
If the anchor is already positioned fully behind the edge of the drywall, it may need to be pushed in and the hole patched, rather than removed from the wall completely. The anchor can be pushed back with a screwdriver and a bit of force. You can also use a hammer to tap the end of a screwdriver or other similar metal object and force the anchor behind the edge.
Drill Them Out
If the rotating anchor has gotten stuck halfway inside and outside the drywall, or otherwise needs to be completely removed, a larger hole may need to be drilled. Use a drill bit larger than the current hole to make room for removal. Once the anchor is accessible, it can be extracted with a pair of tweezers or pliers, and the hole patched and painted or covered.
Patch the Hole
Once the anchor has been successfully removed, patch the hole left in the wall, using joint compound and a putty knife. A general-purpose joint compound works best for small patches. It should be smoothed with the edge of a putty knife, then allowed to dry. Once it's dry, apply a second layer of compound thinned with a bit of water for a smooth finish.