Joseph Stalin was greatly shocked by the Nazi invasion. What I'm wondering is what if that shock was greater than it was in the OTL and Stalin died of a stroke? How would the Second World War have played out without Stalin's brutality?
Molotov is often mooted as a successor to Stalin in a situation where Stalin dies in the first weeks of Barbarossa. I have no idea what sort of head honcho Molotov would be, however.
I suspect that initially, the Politburo would form some sort of collective leadership however, and while as OTL, a way might be found to get Beria out of the picture posthaste, the distraction of the war may preclude the power struggle going further (which may lead to a preference for collective leadership in the post-war period). Also, Stalin dying may actually improve the Soviet reaction to Barbarossa, especially if Stalin dies of this stroke as soon as he hears about the invasion. The USSR is saved from the leadership waiting for weeks while Stalin overcomes his shock, and instead, Stalin is clearly dead and his lackeys are put into a situation where they have to fight for his legacy and their lives and where anyone who acts decisively (who isn't Beria) has a good shot of getting those who are in shock to back them.
And Stalin made enough bad choices in the early stages of Barbarossa that his lackeys have better than 50% odds of making better decisions than he did.
Considering this is the USSR, there may well be a witch-hunt for German spies and assassins as people worry that Stalin has been assassinated by the Germans.
Even if things go worse than OTL, the Germans just don't have the logistics to penetrate much deeper into the USSR than OTL. They may actually reach the centre of Moscow in TTL, but their policies will turn the Soviets against them, will push the Soviets and the Western Allies into each-others arms and ultimately will lead to their downfall.
However, the USSR could take more damage, or significantly less damage, depending on how things pan out. And there is a good chance that once the war is done, absent Stalin's paranoia, the USSR fully integrates into a US-led world order, leading to a significant marketization of the Soviet economy post war and a much more friendly rivalry between the US and their nearest competitor. (Even in a situation where the wartime alliance grows into a postwar friendship, I think there will be a rivalry.)
fasquardon