That is such a sad story and there are likely to be many complexities to it.
Zoe, you can pm if you like and want more info. I will let you know my credientials :)
Physiologically, mothers can certainly breastfeed and breastfeed well even if they are not eating well. Breastfeeding is only likely to fail in the sense of drying up if the mother is chronically and seriously under-nourished before, during and after pregnancy. But sudden starvation might have a dramatic effect - this woman is reported as losing 2 stones in what must have been a very short time, and she may well have seen a difference in her breastfeeding. There's not a lot of research on this - the studies on starvation and bf have been done on populations in famine/food shortage areas, not on individuals in crisis.
Serious stress may well impact on a mother's responses to her baby - and worrying about where you are going to live and what you are going to eat means you just don't have the chance to sit/lie down and feed a baby as often as a new baby wants/needs to feed.