Re:
I am guessing you mean that the broken cap is 'clogging' the thread at the bottom bracket end, not the pedal end, of the crank?
It sounds like it is a plastic dustcap, which the 'face' has broken off, leaving the threads in the crank (this happened to me, with 25 year-old Shimano crank dustcaps).
You need something to grip it from the inside - I used a tool I have for opening/closing quick links on chains - a bit like pliers, but with points sticking outwards at the ends. I stuck it in, opened the jaws, and they gripped the inside edge of the cap. Then turn anti-clockwise, and they were out.
Or have i misunderstood?