One type of registration that would be extremely rare is called an Isolated Chest Registration.
This is where, if completely isolated, one would only have a heavier raw louder sound at the bottom of their voice called chest. The range would be very limited due to no coordination with the stretcher muscle (crico-thyroid). There would be no stretching and thinning of the cords to meet the requirements of pitch.
Now, in good training, sometimes the chest register (arytenoid muscle system) is isolated so the muscle systems can be repaired and reeducated. However, it is not advisable to completely isolate the registers in this process. For the amount of isolation should only be as much as is needed to heal the registers so as to accomplish the goal of unifying the registers.