I have retrieved maybe 20 “permanently” stuck cams, some are on my rack. You may find the following procedure helpful.
1. You will generally need 2 hands, a finger, and a nut tool.
2. Park yourself at the cam, get the belayer to take your weight, place another cam and hang on it, whatever.
3. Study the rock around the cam – how could it have gotten in? Sideways? From the bottom? Does it look like pushing it in deeper will help it move down and out? Think, don’t jerk and swear. Think of it as your kid stuck in a drain pipe. No good abusing the kid.
4. Typically the trigger will be of no use. Try moving the individual cams with either your fingers (using 2 fingers on 2 cams at the same time if you can, or use the nut tool (hook the end around cam and pull). You will find that moving cams directly will be able to close them more than using the trigger. Closing them will free the cam to wiggle.
4. While moving the individual cams, try to pivot the cam clockwise and anticlockwise, move up and down, in and out. This will give a sense of possibilities. Eventually it WILL move out.
5. If it takes more than 20 minutes to free it, you are doing it wrong. Any cam can be removed in 20 minutes. If you get angry, make sure it is at yourself and not at the cam. Don’t bash the rock, work on your technique. If you cannot be patient, maybe you should not be using trad gear in the first place?
6. Enjoy your retrieved (or new-found!) cam. Trad climbing rules!