It is quite common for the element of modern glow plugs to become seized and break during removal, leaving just the tip of the glow plug stuck in the cylinder head.
We were called to a garage for just this problem, they had a Vauxhall Vectra 1.9 CDTi in the workshop to have the glow plugs replaced. When they were removing one of the glow plugs they heard a slight crack and when they lifted the plug out, they found that the tip was still stuck in the cylinder head.
If this does happen, we do not recommend trying to use any drills or easyout type tools as it is likely that these will break making removal almost impossible. The first thing we did was to compare the broken glow plug against a new one to establish the length and diameter of the broken part, this allowed us to calculate the correct size of drill and tap to use. Using special jigs we then managed to drill and tap the broken glow plug tip, then using a special puller we removed the broken section.
After cleaning the glow plug aperture, we fitted the new glow plug, started the vehicle and confirmed the repair was successful.