I had this happen a few times with a poorly-produced batch of .223 reloads (loaded by me) back in the 80's with an Oly .223 when I was a wee teenager.
Sometimes, if the round is close to the chamber or the muzzle end, you can beat it out with a cleaning rod (probably not the best way, and there was a chance of scratching the bore or crown). If that failed, my buddy's uncle had a "bullet puller" that was essentially a large corkscrew on a rod that screwed into the lodged projectile. It was a bear to get the round pulled out with one of those, but it could be done.
Got a ball stuck in muzzle loader once with a light charge. We (probably pretty stupidly) blew it out by unscrewing the nipple and feeding powder into the breech. We got the ball unlodged, and were lucky that we did not blow ourselves up in the process. Damn, teenagers are dumb. Maybe it isn't a bad idea to keep guns away from them without proper adult supervision (which we did not have) until they hit 18 or so. When I think of the stupid things that I did...