KOTY, Ukraine—For decades, gunfire and explosions have not surprised the residents of this small village deep in western Ukraine. The sounds of explosions from artillery training rang out on March 25 from the sprawling Yavoriv military base, the guarded entrance to which lies across the road from the house of Viktor Pokrovskiy. A self-described pure-blooded Ukrainian, Pokrovskiy moved to Koty from his native Russia in 1977. He has heard gunfire and explosions from the military base at Yavoriv for decades, first from the Soviet army and then from the Ukrainian armed forces, which took over when the nation gained its independence in 1991. Even for a man used to the sounds of war, nothing matched the blasts Pokrovskiy heard on March 13 this year when several Russian missiles struck the base, rattling windows in the village and upending the lives of the locals, who had lived in relative calm since …