Peoples Democratic Republic of Israel

The USSR backed Israel early on in its days, because Zionism had a huge socialist flair, and Stalin thought that he could control it. Israel instead identified with the western countries, and the Soviet Union backed the Arab states. Make Israel a communist state with a POD no earlier than 1917. Bonus if you can make it survive to the present day as a Jewish state.
 
I can not think of one. Despite being influential in the movement that overthrew the Czar, the policy of Zionism conflicted with views held by Lenin and Trotsky. Throughout the entire history of the Soviet Union, the Jewish people suffered from persecution of some sort. The only thing that even comes close to what you are suggesting is the Jewish Autonomous Oblast that was set up in the Far East, in order to counteract Zionism and place it within the communist sphere. It was a complete and total failure, and whatever progress was made was largely reveresed during 1930's purge by Stalin.
 
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