At 8 p.m. on Saturday, a jury deciding the racially charged manslaughter case of a black man who shot a white teenager last year was still “hopelessly deadlocked,” to use the term the jurors used earlier in a note to the judge. It was the 11th hour of the fourth day of jury deliberations, and a pack of news crews was waiting, as were lawyers, anxious relatives of the defendant and the victim and a racially divided gallery that had sat on separate sides of a courtroom in the Suffolk County courthouse for a month. A mistrial seemed imminent. But...