@Robot_Ditto
I didn't get the impression that one was purposefully starving herself, but rather that she was already on the verge of death and had lost all appetite, and the other was "making up for it" as they always did out of habit. The brainwashing means they're not really treated as human or would think of survival like we would, but even with humans on the verge of death and exhaustion people often stop eating.
As far as why, the soot sickness can apparently be quite fatal, it was remarked that the "sendoff" often amounts to a death sentence. So just bad luck that one made it and one didn't, or from another perspective good luck that they didn't
both die. Maybe she took in slightly more soot, got attacked by clingers a bit more often, or the water treatment worked slightly less well. They were both on the edge and she stepped over it while the other didn't quite. So it goes sometimes with toxic exposure. Like if you breath low levels of asbestos or ingest low levels of heavy metals or PCBs or whatever, there is a chance you develop cancer but it's probabilistic not guaranteed. A lot of people will suffer/die so we have standards around it, but every once in a while you'll find a coal miner or someone who smokes a pack a day and drinks with abandon or whatever who lives to their 80s/90s. The average life expectancy is a lot lower than regular population, but over enough people some will happen to get really lucky.