Yeast would be an air contaminant that would get into the liquid and grain. Once they had a contaminated batch that turned out well, they would keep a small portion to put in the next batch. Or before they figured that out they would just reuse the contaminated container which would innoculate the new batch without their even knowing it was happening. Kind of like making sourdough bread with sourdough starter. Make your bread, keep a little dough in a cup in the fridge, and mix it with more flour and water to make your next loaf. During the depression, my father lived in the mountains of Arizona running a trapline, and always kept his sourdough starter handy for breadmaking.
(When most people realize that women always made the beer, and somebody says "don't ask about the yeast", the first assumption is a bit different from yours. Rather disgusting, actually. But it was spit).