Captain Aya was the Commander of the Varia. You find her in a critical state from the crash in the Flight Deck. She has a support beam from the ship stabbing into part of her lung. Pulling the support beam out will lead her bleed and consequently die.
In order to save her, the first room you must go into the Flight Deck. There, you must leave the support beam in, if you remove it this will cause her to bleed out and Taylor to panic thus leading Aya to die. Keeping the beam in, have Taylor look for a med kit. Later, you will be told about a stasis pod that can help Aya. Moving the pod to Aya will allow Taylor to help her, but the game will give you the option to power the pod or the beacon. If you wish to save her, power the pod instead. Powering a beacon does not help because when Taylor is in the room in the peak, he will eventually find a ship crossing their sector and send an S.O.S message to them, getting him and Captain Aya saved(This happens when you choose to power the pod).
Moving Aya to the pod will cause her to bleed more and die, removing the support beam will have the same effect.
[If you choose to let her die/do not check the Flight Deck on day one, she will later appear being possessed by the aliens depending on your choices.]