I was just putting a low mileage motor back into my 2000 tdi and said why not replace all the glow plugs while it is out on the stand. Mistake. Now 3 out of 4 glow plugs came out easy but one snapped and just turns. I broke off the head of the plug so I could drill the plug for an easy out. But no luck still stuck. Can I heat up the plug and head a little so maybe th PB Blaster can work better? Any tricks in the TDI bag?
Try the heat, yes.
If any peices end up in the cylinder do not start it!
You may end up needing to pull the head.
That's kind of a problem with TDI's .The glow plugs last so long that when it comes time to change one it can be a disaster. I had one guy in this week with a 98 and he's was pretty sure none were changed for at least 6 years
so..
1) the threads unscrewed, then the swollen tip broke?
or
2)the hex broke off the thread portion?
1) combustion pressure will sometimes remove it
2) Weld a nut to the remains and unscrew?
Got it out!!!

Heat and jammed a torks bit into the drilled hole and closed my eyes. Heated with a very thin flame then let it cool. When I felt it give I was so happy for not having to pull the head. Got lucky this time!
I think welding is removing is your best bet.
I was just putting a low mileage motor back into my 2000 tdi and said why not replace all the glow plugs while it is out on the stand. Mistake. Now 3 out of 4 glow plugs came out easy but one snapped and just turns. I broke off the head of the plug so I tires cars could drill the plug for an easy out. But no luck still stuck. Can I heat up the plug and head a little so maybe th PB Blaster can work better? Any tricks in the TDI bag? 