How does Vladimir die in the novel, All the Winters After?

One night, while Kache is performing with his band at the bar, Vladimir goes to the homestead where he has been stalking Nadia and holds her hostage with a knife on the edge of a canyon. When Kache approaches with Nadia's dog Leo, the two of them are able to distract Vladimir while Nadia pushes him over the edge. Kache descends the canyon and finds Vladimir mortally wounded. He then shoots him to end his suffering.