What if Japan were like the Korean peninsula wherein it is split in half with the anime-crazy democratic wonderland and a backward communist totalitarian nightmare? It almost became a reality if the U.S. did not had the atomic bomb or decided not to use it. With politicians and military leaders failed to make a consensus over the implementation of Operation Downfall - the Allied invasion of the Japanese home islands, the Soviets decided to launch their own version instead.
As the war drew to a close, the next conflict was already emerging, with the Soviets and the rest of the Allies each trying to gain control over the defeated Axis countries. That is, of course, why some wound up getting divided, like North and South Korea and East and West Germany. Well, that exact thing almost happened to Japan.
During the final days of the war, the Soviets unleashed its fearsome steamrolling army into Japanese-controlled Manchuria to push the thinly-spread defenses back. This was part of a massive Allied invasion plan that was launched on the same day as the United States dropped an atomic bomb on Nagasaki. Experts believed that the Soviet Union originally had no intention of stopping at Manchuria. It was supposed to be dry-run of a full-scale invasion of Japan itself, which would've seen the Red Army dance the mamushka in the war-torn, smoldering Tokyo ruins.
It was envisioned that the Soviets would invade in the north before Operation Olympic and Coronet would commence. By late August 1945, the invasion force would reach Hokkaido two months earlier than the scheduled Allied 'Normandy'-type beachheads. However, Stalin kept his plan a secret from the other Allied forces and had absolutely no intention of telling them anything about it, preferring to wait until the forces of Operation Olympic stormed the shores of Japan to find him sitting in the emperor's palace watching cartoons. It is likely that Japan surrendered not because they were afraid of more atomic bombs from the U.S. but because they were afraid of the Soviets.
So what would have happened if Stalin had managed to plunge his forces into Japan before the war had ended? We'll never know, but based on how it went down with the other disputed territories, it's easy to guess. Stalin would've had a legitimate claim to, if nothing else, split the island in two once the war was over, maybe with a North and South Japan (possibly even a partitioned Tokyo), with a hotly contested border constantly patrolled on either side by varying groups of aggressively non-Japanese people.