It can happen after one fateful event—a civil war, natural disaster, or brutal takeover—or insinuate itself gradually, like a cancer that eats away at a country for decades. But when a nation is failing, you see it in the eyes of its people. Over a billion people live in countries in danger of collapse. Some leaders lose control over their territory and cling to their capitals while warlords rule the provinces. Many governments are unable or unwilling to provide the most basic of services. Most are hobbled by corruption and environmental degradation. Such unstable states are dangers not just to...