Many different types of wall anchors are used, but not many solutions exist for removing a screw that has become stuck in a wall anchor. When a screw gets stuck in an anchor, the anchor usually turns with it when you try to back it out, which can lead to various levels of frustration, depending on whether the anchor is simply embedded in the wall or has wings holding it to the back.
Types of Anchors
Wall anchors can be metal or plastic, and screws are equally capable of becoming stuck in either type. Plastic expansion anchors can be conical or straight, and they wedge against the hole when you drive in the screw. Additionally, some plastic anchors have wings that expand against the back of the drywall. Metal toggle bolts have a similar design. Another type of metal anchor, the molly bolt, has an expandable sleeve that functions like a combination of an expansion and a winged anchor. And some metal and plastic anchors have threads and simply screw into the wall.
Hold the Anchor
If the anchor is turning with the screw, you can usually loosen the screw by holding the anchor steady with a pair of needle-nose pliers. You can do this as long as you can see the rim of the anchor. Work the tips of the pliers around the rim, and squeeze tightly while you back the screw off. You may have to chip a little of the wall material to get a good grip. If the anchor is metal, spraying a little lubricant behind the head of the screw may help to loosen the threads.
Apply Outward Pressure
If you can work the tip of a slot screwdriver behind the head of the screw, you can usually wedge the wings of plastic winged anchors and toggle bolts against the back of the drywall by prying the head outward. In many cases, the wedging force is enough to prevent the anchor from turning with the screw. If you apply this kind of outward pressure on an expansion anchor, you're more likely to pull the anchor out of the wall than to unscrew the screw, which is probably preferable to leaving the screw in the wall.
Cut out the Anchor
Cutting an anchor out of drywall is a last resort but may be your only option if you can't stop the anchor from turning. This strategy is usually necessary just when you are dealing with winged anchors and toggle bolts because you can almost always pry out expansion bolts. Make the hole as easy to patch as possible by cutting as close to the anchor as possible with a utility knife. Score about halfway through the drywall, then tap the screw and anchor through the back of the wall with a hammer. Patch the hole with patching compound and drywall mud.