How can I remove 1/2" PVC pipe that has broken off inside a 1/2" elbow?
You know what they say: nothing is forever -- except glued PVC parts. Well I don't know if they really say that but they should.

It's unclear exactly what situation you have, but if you have a glued part that is broken, the only option is to cut out the elbow and replace it with a new one. You might need to use a coupling to add on another 1" or so of pipe to get the elbow positioned correctly again.