Baby Natalia was born with almost no brain

Baby Natalia was born with almost no brain(part of the skull and cerebrum was missing) and therefore will never develop the functions we associate with being human such as thinking, talking, reasoning and planning. She survived for 9 days because a very primitive part of her brain was functioning to keep her alive.

Questions:

What is this condition called?

Which part of her brain kept her alive for nine days?