Claire can be found outside her flaming house in the northwest corner of Aleroth's Crow's Nest district during the events of Divinity II: Flames of Vengeance. You may wish to save the game before approaching her, since you only have one chance to accept and successfully complete the quest she automatically offers (which is on a strict timer and will likely take several attempts to perfect).
Claire is a psychiatric patient at Wild Willows Manor being followed by Doctor Bernard of the Aleroth Healers' Guild. She lost her baby in a zeppelin accident, and now suffers from what Bernard calls "newbornophilia," meaning that she is in denial about her baby's death and projects its image onto other babies. She has since adopted a baby imp, which soon died of malnutrition. Details of her illness can be read in Bernard's therapy report, which can be found in his room at the Healers' House.
And it Burns, Burns, Burns – You find Claire's House on fire, with a distraught-looking Claire standing outside. When you approach, she automatically engages in conversation and asks for your help. After explaining that as a Dragon Knight you're more adept at starting fires rather than extinguishing them, she informs you that her baby is trapped inside. While you're in there, she'd like you to attempt to salvage her love letters and wedding ring as well, if possible.
If you refuse to help her, she braves the fire and enters the house to rescue the baby, only to be killed by an explosion shortly after.
If you accept the quest and fail, she remains outside the house but can no longer be interacted with. If you accept the quest and succeed, she leaves the area.