One type of registration that would be extremely rare is called an Isolated Falsetto Registration.
This is where, if completely isolated, one would only have a falsetto sound that is a light breathy soft sound on a few notes within this tonal range: B below middle C to the B above. The vocal cords would be openish with no real volume or power possible due to no coordination with the closer muscle (arytenoid). There would be no closing of the cords. It would be like trying to step on a cloud versus a flexibly firm platform.
Now, in good training, sometimes the falsetto register (crico-thyroid muscle system) is isolated so that 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.