There have been brain studies in which they looked at the effect of lesions on function. And it seems there's no single area that maintains "the self". And often, if one area is damaged, the brain tries to adapt and move some of that function in other areas, to compensate.
Which begs the question where is that self integrating sensory input and producing thoughts and actions. Because brain lesions seem to only impair the flow of information, not the possibility of function.