I recently learned of the Holodomor from an eye opening lecture on-line by Harvard Professor Timothy Snyder (nothing fancy: youtube). the holodomor was a man induced famine in the Ukraine in 1932-33 during which 3 million to 7 million people died of starvation. Stalin famously would not allow aid to reach the population, and people who tried to flee were shot. This starvation killed Ethnic Ukrainians and Jews with total indifference. If you find no traces of your family they may have been victims of this Soviet era induced starvation. Most people who were buried did not have grave-stones, many more were not even buried. The fact that the real number remains unknown is an indication of the inability of locals to record the deaths in any systematic way. I believe that there are no records of the deaths in the Jewish community.
All the best,