How did Balaam son of Beor die?

Answer: Killed by Israel with the sword

When Israel fought Midian, they killed the five kings of Midian and also Balaam son of Beor with the sword.

“Among the slain were Evi, Rekem, Zur, Hur, and Reba—the five kings of Midian. They also killed Balaam son of Beor with the sword.”— Numbers 31:8 (BSB)