The answer: nothing, if the mother was smart enough to just keep nursing (assuming baby is under 6 months old).
Breastfed babies die in famine situations all the time though right? Yep. Because the mother is so desperate, so unable to believe that she can provide adequate nutrition when she herself is wasting away, that she will feed the baby anything. Women have been known to chew tree bark and grass on the side of the road and feed the nutrition-less pap to their babies because of that insecurity.
The truth is, nature is a smart cookie and survival of the species is a pretty strong genetic need. Baby gets the choicest nutrients and the composition of breast milk changes to give baby the best chance of survival, even over the mother. Nursing takes so few calories from the mom that even if she is skeletal and malnourished, baby will be fat, healthy, and happy if nursing continues. Women even managed to nurse babies and keep them alive in the Nazi concentration camps, under the absolute worst conditions.
If, however, mom decides to supplement baby on whatever food can be found, then baby will likely become as malnourished and skeletal as the mom and may die rather quickly. Artificial baby formulas aren’t a safe bet either, in modern famine situations. Diarrheal illness is widespread during famine, and without clean water, refrigeration, and proper handling, formula can be every bit as deadly as famine.
Older babies >6 months need some supplemental nutrition, but breastfeeding is still vitally important, as mom’s immune system continues to help baby to fight off any pathogens mom is exposed to – including those diarrhea producing bacteria that can rage through refugee camps and the like.
In your fantasy stories, if mom is lost, baby can still survive these conditions if someone is willing to become a wet nurse. Anyone female with breasts will do for starters – any woman can breastfeed. However, pregnant women will only produce colostrum – an immature milk in tiny volumes that won’t support a growing baby’s needs fully. Establishing a milk supply in an individual who has never been pregnant is a little harder than in someone who has made milk before, but it can still be done. Putting baby to breast frequently, stimulating the nipples, and some herbs (with limited efficacy) have been long-known to restart or start lactation. In modern times, the American Academy of Pediatricians recommends that adoptive mothers of young infants breastfeed. However, wet nursing and milk exchange is highly discouraged in the US today because of the risk of spreading diseases like HIV.