Swallowing a bullet could lead to lead poisoning and cause you to eventually die a slow painful death overtime.
You usually won't die soon after but it will most likely take a few months to maybe even a year to die of the lead poisoning.
The bullet certainly won't go off in your stomach though but you do require surgery to remove those cartridges or bullets from your digestive tract if you swallowed either a bullet or cartridge.
If you do not get surgery to remove the bullet from your stomach then the lead gets into your blood stream and can cause death overtime.
So if you do swallow a bullet which you really should never do you need to get to the emergency room or urgent care soon after to prevent lead poisoning.