Chapter 6 of Sweet Darusya referred to the "unavoidably-raised ax of history over every person's head". What does this phrase mean?
Dangling axe, or dangling sword, is a maxim that refers to Damocles.
It generally means something inevitable and/or looming.
It was — and it is — widely popular in Ukrainian literature, politics, and even colloquial speech. Daresay, literally everyone here in Ukraine knows its meaning.
The connotation to the ultimate power of history is explained in great detail in Mary's excellent answer.
It was a great principle of Marxism that they were the wave of the future and how History was going and their triumph was inevitable.
Which meant that everyone in the Soviet Union had a duty to contribute, and if History did not turn out as expected, it had been sabotaged. The saboteurs -- the kulaks, the hoarders, the wreckers -- had to be ferreted out and sent to gulags to keep them from stopping History. And if your village were one to fail, anyone in it might be targeted.
Consequently, there was no way to avoid the knowledge that anyone could be hit by the claim they were preventing History from unfolding in Marxist lines -- like an ax hanging over their heads.