It’s easy to forget that cities like Penza, near Russia’s Volga river, even exist at all. More than 400 miles southeast of Moscow, it is best known for its singing cuckoo clock and the country’s first ever Stalin Centre, complete with a golden bust of the communist dictator.

And yet half a million people call the city home, around the same number as Atlanta or Sacramento. Neighbors chat with each other, newlyweds search for apartments, kids play together in the street, and families head out to the woods on the weekends to pick mushrooms and swim in the lakes. Out of the eye of much of the world, whole lives are lived here.

Penza’s once thriving high street has fallen into a chasm—just a literal chasm, with municipal authorities digging a colossal trench through the middle...