In the shop I used a tap; a purpose-made shell extractor is best, of course, but they are caliber specific and a shop would need a half dozen or more.
There is a remote chance of cutting through the case into the chamber wall, but you are using only the fingers to turn the tap, not a wrench, and I never had any problem.
I have also used a brass brush in a cleaning rod (regular cleaning brush) inserted into the broken shell from the rear, then pulled back out with the bristles grabbing the shell. (A .45 pistol brush works for most .308 size cases.)
Jim
There is a remote chance of cutting through the case into the chamber wall, but you are using only the fingers to turn the tap, not a wrench, and I never had any problem.
I have also used a brass brush in a cleaning rod (regular cleaning brush) inserted into the broken shell from the rear, then pulled back out with the bristles grabbing the shell. (A .45 pistol brush works for most .308 size cases.)
Jim