Brod is Jonathan's great-times-five-or-six grandmother, and the story Jonathan (the character) comes up with surrounding her is almost too wildly supernatural to be true:
Brod bobs to the surface of the river (the river Brod, which the baby is named after) after Trachim's wagon sinks. No one even knows who her real parents are. (Whether or not Trachim even had a wife is up for debate, although the old perv Sofiowka swears he remembers Trachim's wife's perky bosoms.) She had no umbilical cord (3.8) and she has "perfectly adult features" (3.19). Where did this baby come from? Did it hurt when she fell from heaven? Are the Volturi going to come after her?
Whatever the story, Brod has trouble adjusting to life on land. She has no friends her own age growing up. She's vegetarian, which was as weird then as it is weird to Alex now. Oh, and she's also "a prism through which sadness could be divided into its infinite spectrum" (11.30). So, there's that.
Guys, Brod is really really sad. Maybe it's because she's basically a supernatural character who doesn't know how to fit in on this earthly plane, but much like an emo teen, she spends a lot of time cataloging her sadnesses. She comes up with 613 sadnesses, including these:
Some of these feel like sadness wrapped in sadness. A sadness burrito. A sadness turducken. A sadness—you get the point. It's sad.
At least Brod has an excuse, unlike the emo teen: a lot of really bad things happen to her. Aside from the whole possibly magical birth, she's raped by the town lunatic, Sofiowka, on the same Trachimday (a town festival) that Yankel dies. On that day, she also meets her husband, the Kolker. Talk about fate!
Alex calls Brod "a good person in a bad world" (14.12). We're not sure what eventually happens to her, or even how she died, but we do know that Brod's life is like two mirrors facing each other. In her infancy, Yankel keeps her in a bed of newspaper in the oven, and the newsprint tattoos itself to her body (is she made of Silly Putty?).
And then, when she dies "her diary's wet pages printed the sadnesses onto her body" after she was "recovered" (24.109) from wherever her body was, which we're pretty sure was someplace wet.
Perhaps she simply disappears into the same water—or the writer's imagination—whence she came.