Dogs, cats, and other animals have what is called a “dewclaw.” It’s the first digit or toe located on the inside of the leg above what we would think of as the wrist or ankle.
Some dogs have them only on the front paws, others have them on all paws, and some may have more than one per paw. Dewclaws can seem attached very loosely to the paw with just a flap of skin, or can be more firmly attached. Either way, it is a live digit and the nail does grow on it. Because it is higher up on the leg and usually doesn’t make contact with the ground when the dog or cat is walking or running, the nail will grow unchecked, and should be trimmed frequently.
Some people prefer to have the dewclaws surgically removed to prevent any problems such as it getting caught on something and getting ripped off accidentally. Some have them removed to comply with breed standards. Others just leave it alone. I am of the opinion that they should be left alone. Especially for cats, in which they do use their dewclaws to help them grasp onto things. If you want to read about the pros and cons of declawing a cat.
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Most of the time, dewclaws are removed when dogs are puppies just days old and a local anesthetic is used. If the dog is older, more caution is necessary because general anesthesia would be used. The surgery itself is not complicated, but as with any surgery, there is always risk of complications with anesthesia or infection at the surgery site.
After surgery, the paws will be bandaged for a few days and stitches should be removed in about a week. The incision site should be observed for signs of infection (redness, swelling, discharge, pain).
As with any medical procedure, have a discussion with your veterinarian about the pros and cons before you make a decision to have your dog’s dewclaws removed. I know of a dog who has had them removed and has never had any lasting problems.