To build on /u/Doctor_Impossible_ answer, the person usually counted as the final casualty in the war was a US soldier, Henry Gunther who was taking part in the Meuse -Argonne offensive. It was a joint offensive by the US and France. Gunther apparently died at 10:59.

But France especially was pushing for these advances up until the last minute. They had suffered extraordinary casualties and now that they had US reinforcements, new and better tactics, and restored morale they were trying to get every benefit they could out of the fighting before armistice.