Shalom is from the village of Kolki, just like Alex's grandfather. Unlike Alex's grandfather, Shalom wins the Trachimday competition in which people dive into the river to retrieve bags that are supposed to represent Trachim, who might be Brod's father. (Yes, Everything is Complicated might have been a better title.)
On the night that Brod is raped and Yankel dies, the Kolker is illuminated (ahem) by a bolt of lightning, showing Brod that the Kolker is watching her through the window as she undresses. Instead of calling the shtetl SVU, she finds this romantic. In fact, as we find out much, much later, she finds it so romantic that she asks him to kill Sofiowka.
So what does the Kolker do? Hangs Sofiowka from the bridge: "Across his chest was written, in Brod's red lipstick: ANIMAL" (24.88).
That's one way to prove your affection, huh?
Despite this auspicious beginning, their marriage is kind of a bummer. Brod never talks to him, just mopes around all the time, and won't even talk about why they don't talk. Then, one fateful day (emphasis on "fate") he's a victim to the flour mill curse… but it doesn't kill him. It just ("just") leaves a saw blade implanted vertically in his forehead.
This little accident changes the Kolker (like when Phineas P. Gage ended up with a rod through the head) and makes his tense relationship with Brod even more difficult. He yells at her about his socks, punches her while they're in bed, and is generally an abusive jerk. (Brod: "Why did I marry Charles Saatchi?!")
Oddly enough, though, the little punching incident ends up improving their marriage. He locks himself in a room, presumably to protect her from himself, so Brod only sees him through a hole in the wall. (Symbolism snack: this is kind of like how people only saw her through a hole in the wall when she was a baby). Anyway—NSFW alert—it's a good thing that he "like[s] making love from behind" (16.15) because that's how he has to do it through the hole.
Even though they can only see pieces of each other now, they can communicate physically and emotionally in a way they were never to before. This leads to some blunt conversations. Brod admits "I don't love you" (16.161) "because I couldn't love" (16.183). Guess marriage didn't cure any of her 613 sadnesses, huh? She's not totally cruel about it, though. She tells him, before he dies, "I'm sorry that this has been your life. Thank you for pretending with me" (16.241).
In the end, Kolker dies, even though Brod renames him Safran in an attempt to trick death. Funnily enough, her third child, the one who lives long enough to continue the line, is born the moment the Kolker dies.
Could this child possibly be the Kolker reborn? Hey, why not. It wouldn't be the strangest thing that happened in this book.