Jessica Maxson is the mother of Arthur Maxson and wife of Jonathan Maxson.
Background
She and her husband died when their son was still very young, making Arthur the last of the Maxson Dynasty at the time of Fallout 3. Her husband Jonathan was killed in battle as a Paladin[1], but the cause of her death is not specified.
Appearances
Jessica Maxson is mentioned in a terminal at the Citadel's library in Fallout 3. She does not actually appear in the game.