Is it ever possible to auto-rotate with a missing rotor blade? A couple of years ago a UH-60 managed an auto-rotation landing with "badly damaged rotor blades."  (Couldn't find further details on that incident.)

Is it ever possible to auto-rotate in a helicopter that has lost a segment or entire blade of a main rotor?

My guess is that, in general, it would be impossible to control the lift asymmetries and such in-flight damage would always result in an uncontrollable crash.  If that's correct, then what about the special case of a helicopter with 4 or 6 main rotor blades, and if it were possible to jettison the blade opposing the one that was lost or damaged?  (Are any helicopters equipped with an emergency ability to jettison rotors in flight, other than the ones with vertical ejection seats?)  Is it known whether such a damaged rotorcraft can reliably auto-rotation in that scenario?
Highly improbable. If you've ever seen how much a washing machine can shake with a little imbalance in the laundry, at a relatively low energy spin, imagine the destructive forces that would be experienced by the imbalances in your theoretical rotors. Even if your missing blade manages to get away without causing impact damage to the other blades, there is going to be an immediate violent force translated through the aircraft. Your newly configured rotor formation is still going to try to spin around its center of mass, which is no longer concentric with the mast. The degree of imbalance will tell you how far off center the new center of rotation wants to be. The mast is still going to be trying to keep the rotor rotating on its own center, so now the rotor and mast are fighting to circle their common center, and basically this means the rotor, it it doesnt just go to pieces from all this force, will be yanking HARD and fast on the mast, which would probably rip it off the airframe.... but, if your magic rotor and mast stay intact, the violent motion would be translated to the airframe which will now be shaking super violently around you, which would likely cause it to rapidly disassemble. If it magically stayed together, the people inside (hello pilot) would be experiencing forces through the body like riding the paint shaker at the hardware store, but harder and farther, if not faster, on every shake. Watch that paint shaker and imagine your head being in that. 

I do not believe your scenario would be survivable, even on the ground. It's odd to think, but a complete rotor disintegration is not the worst thing that could happen after blade loss.