The way I think of it is along this way:

Despite the fact that our brains consist of bilions of neurons we think of ourselves as a unit enclosed in a single skull. But studies on people who have two sides of brain separated suggest that there can exist two separate conscious entities in one body.

If we have removed the physical limitations of support systems of our brain - I think it is possible you could split the brain in smaller and smaller chunks of less and less conscious entities until you reach single neurons which almost certainly do not have consciousness.

"The_Invincible" from Stanisław Lem is also a nice novel about the similar concept.