Normally, when someone is blind, there is something wrong with their eyes. But, sometimes someone is blind because there is something wrong with the part of the brain the processes visual input, such as a brain tumor or damage to that area of the brain from a traumatic brain injury or stroke.
It is also the case that the brain is "plastic" which is to say that sometimes, if the part of the brain that normally handles some function is broken, the brain can rewire that part of the brain to do something else.
For example, in almost all mammals that can see in a full range of colors, the part of the brain that processes color was repurposed from the part of the brain that handled the sense of smell before the mutation that allowed for additional cones in the eyes to improve color vision. Indeed, in some species, the color vision mutation has not reached fixation, so some individuals in the population can see in color, while others cannot. In those species, one can see the repurposing of areas of brain function originally allocated from the sense of smell to handling color vision on an individual level within the population.
So, the seeds of possibility are there for a recently documented case of a woman who developed blindness in connection with a traumatic brain injury, and also (it isn't entirely clear if this happened before or after the traumatic brain injury) developed multiple personality disorder (currently known formally as dissociative personality disorder or "DID" for short).
This women displayed the classic symptoms of DID, switching in all sorts of mannerisms on a dime from one "alter" to another. But, a funny thing happened. While most of the alters were cognitively blind, some of her "alters" could see perfectly well. EEG measurements of her brain confirmed that indeed the blind alters were not processing visual information, while the seeing alters were processing visual information, corroborating the patient's account.