Reading between the lines of the OP, I suspect that the OP's issue isn't with the shank (tubular extension) of the nipple, but with removal of the head which is recessed in a double wall rim.
He describes the shank as broken, so breaking it more won't help. Possibly there's enough left that he can grab and turn it with pliers or a vice-grip, but if not, he still has to remove the head, and if he breaks the shank off completely won't be able to turn it from that end.
Ultimately he'll need a purchase on the head itself, either with a screwdriver slotted to clear the spoke, or with long nose pliers, or some other way. My method of detensioning the spoke will reduce the needed torque and help with whatever method he uses.
One more method he might use.
Find or buy a socket wrench or nut driver which is slightly too small to fit over the head. Using a bench grinder, spin grind the OD at a shallow angle to form a circular chisel point. Tap it down over the head and it'll shave the head to a hex, then use a fresh nut driver to remove the now hex shaped nipple. (Do not try to drive it with the cutting edged tool whose thin walls will fail.
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