How to get broken pin out if 8 1/4 chunk?

Sometimes I have been able to take a pick when there is like a 1/4-1/2 thread left in the carrier and catch an edge of the remaining stub, and twirl it out as many times when a bolt breaks there's an edge left that a pick can catch and with no head left on the stub (it already unscrewed right) there is no pressure/torque left on the stub...