This is a common question we hear more and more with the resurgence of diesel engines. There a few reasons they break while trying to remove them
Old age. Older glow plugs swell up and are not able to be removed from the cylinder head. They will unthread until the swollen portion does not allow it to come out with drill and extracting. On engines that do not have on-car kits for extracting require the cylinder head removal to send to a machine shop.
Electrical failure. When the glow plug activation circuit sticks and keeps the glow plug powered up, remember once started a diesel uses the high compression detonations to run, the end will mushroom and will not be able to be removed.
Mechanical failure. When an injector drips fuel it contacts the glow plug and it can cause it to mushroom also. Worst case scenario when fuel drips on the hot glow plugs they break and the pieces bounce around the chamber and can make their way down in to the cylinder and cause damage to valves or pistons.
How can this be prevented?
What are the replacement intervals of glow plugs?
Some manufactures have replacement intervals of 100,000 miles, or when they fail. The way to prevent this is to change the glow plugs every 30,000 miles before they fail and have the electrical circuit and fuel system operating correctly.
For Mercedes there are glow reamers for cleaning built up carbon in the chamber when replacing the glow plugs. These are available from Baum tools for diesels from the early 1980s to present.
Replacing the glow plugs regularly is more economical then dealing with broken glow plugs later. As with any piece of machinery they function at their peak when they have preventive maintenance.