When Nina was sent to the Dome by Presper as a grad student, she made the mistake of taking her suit off, and consequently got sick. She was put to sleep, in cryogenic storage, to keep her alive. She has an obsession with Goddard, going so far as to shave her own head.
Goddard is unaware of Nina's father figure dependency on him, and now that she's comatose, he's more irritated by her presence than anything else. He almost wishes she would choose to die one way or the other so Agnes can spend more time on other matters - he realizes that he can't say this because of the reaction of the others, but he's definitely thought about it more than once.