I think the Doc called it the tuft of the bone.
Worst part was the second or so when the bit was turning inside my thumb... it took a second for me to pull the drill back & get my finger off the trigger, so it got several revolutions before I got it out.
Luckily it was a cordless that didn't have that many RPM's... an electric drill would have probably gone down to the first joint.
I've drilled into & broken several bits in my fingers before, just nothing this bad.