What term describes people that cannot feel pain? I remember a case study about a girl who could not feel pain due to lacking certain somatosensory receptors; she went on to burn herself on a radiator because she could not feel her flesh burning and suffered many other injuries due to the loss of the sense.

What term describes this deficit?
Analgesia is the term used for inability to feel pain.
Hypoalgesia is the term for low sensitivity to pain.

Hereditary sensory neuropathy and Congenital insensitivity to pain are two known syndromes that contain these deficits as their symptoms.