His books were readily available to read in USSR. They were studied as any ideologies would be studied.
There is a great story Michael Parenti used to tell about a trip he took to USSR. He was with a bunch of American academics, who had been talking down on the Soviets and the censorship they guessed they had been under.
When one of them asked a Soviet academic which western theorists he’d read, he rattled off a long list, which both Friedman and Hayek were on. The Soviet then asked the American which Soviet theorists he’d been able to read.
And the American couldn’t list a single one.
That story is a perfect encapsulation of how real, effective censorship works. You’re not outright forbidden to read. You are, instead, gaslit into it with billions of dollars worth of propaganda, information marginalization, distortion, and lies.
This is why you still find people today who believe in cartoons, rather than simply opening their eyes and looking at the real world, who retreat into safe abstractions rather than face the cold, hard reality that we are the most propagandized, socially engineered, and brain washed people in history.