Actually when arguments were presented, well argument by the Government, he was alive. He was killed, with a .38, a few weeks before the decision was announced. But even if he had been dead, there was his former co-defendent, Frank Layton, who should have been represented at the Supreme Court. He or they would have been "respondents", not defendents, just as "Heller" is in the current case. The government (US or DC) being the one who asked the Supreme Court to review the decision of a lower court in each case
Read all about "Miller" at this collection of court and other documents
But here is the part that address's Miller's death and Layton's "disposition"
The Southwest American reported on April 6, 1939, that Miller's body had been found in the "nearly dry" bed of Little Spencer creek, nine miles southwest of Chelesa, Oklahoma. He had been shot four times with a .38. Miller's ".45 calibre pistol," from which he had fired three shots in his defense, was found near his body. He was forty years old.
The indictment had been quashed by the district court judge on JANUARY 3, 1939. The government petitioned for appeal directly to the Supreme Court January 30, 1939. The government's brief was filed in March of 1939, Oral argument was presented March 30, 1939. The decision was released May 15, 1939.
One of the documents in that collection is the government's brief in the case, it contains many of the same arguments presented by DC and by the US solicitor general in their Heller briefs, most of which the Court ignored.
Little was reported regarding Frank Layton. He pleaded guilty to the charge of transporting a sawed-off shotgun after the Supreme Court decision and was placed on five year's probation by Judge Heartsill Ragon on January 8, 1940.
Thank you both for the addidtional information and clarifying things.