Q. Who is that "I" if consciousness is in the brain? Why does the brain die if it is the seat of consciousness?
A. From the First Mind perspective, consciousness feels as though it is restricted to the brain and/or body. The "I" in this case is the local, personal sense of identity–"me"–sometimes referred to as the ego in spirituality.
It is not that consciousness is actually in the brain, nor produced by the brain. (See the evidence here.) Popular theories of consciousness like integrated information theory and global workspace theory are neuron-based First Mind theories, and therefore also support the notion that consciousness is brain-based.
From a Second Mind perspective, however, the brain and body, along the world of particular objects, events, and relationships, are representations of non-local consciousness. Here, "I" refers to non-local consciousness, which also represents itself personally while not being restricted to only one kind of identity experience.
The death of the brain is compatible with either view. The First Mind view can continue even after the death of the brain and body, however this is usually not recognized while the body is alive given educational biases in our world culture. Therefore, whether one recognizes non-local identity and its relationship with the world of matter prior to the death of the body or not does not affect the continuation of consciousness after the death of the body.