A "worm" is a tool used to extract a round out of the barrel. They are used in cannons as well as rifles that are loaded from the muzzle. If the powder does not fire, then you can remove the ball from the barrel by pulling it out. The tool is inserted and the tips grab onto the ball so you can extract it. I have done this with my rifle which fires soft lead. I'm not sure how easy this is to do with a large cannon ball made of steel.
Another type of "puller" used for rifles is a screw instead of a "worm".
Here are two photos of Civil War dug relics that show a rifle bullet that has been extracted with a worm and with a screw.
Thank you! This previously posted photo was most useful (see below). I can see how such a clamp could work. And given, as Dave says, we are dealing with iron and not steel (and iron is in short supply), there would be attempts at repair.
Antique Ordnance Publishers …. publish reproductions of measured drawings that were provided to manufacturers in the mid-1800s to manufacture Traveling Forges, cannon carriages, and other carriages for the U.S. Army
Go to: http://gunneyg.info/html/AOPCatalog.htm