BELGRADE — After 15 years on the run — sometimes in plain sight at soccer matches and weddings and sometimes deep in the fabric of this secretive city — Europe’s most wanted war-crimes suspect, Ratko Mladic, is being hidden by no more than a handful of loyalists, most probably in a neighborhood of Communist-era housing towers, according to investigators and some of his past associates.

The diminished circumstances of the former Bosnian Serb general, who once was protected by scores of allies and Serbian government officials, make him ripe for capture, according to these people. But a softening by several European countries on whether his arrest should be a prerequisite for Serbia’s admission to the European Union is raising questions about whether he will ever face justice.

These developments make this a seminal moment not only in the search for Mr. Mladic but also in Europe’s often agonized deliberations over how much to encourage the manhunt in the face of deeply conflicting priorities. In the name of unity and stability, should Europe put a premium on rehabilitating a battered country that became a pariah state in the Balkan wars of the 1990’s?...