For Larisa Shchetinina, now 72, the decision to leave Ukraine — though not the act itself — came suddenly. In 1992, she went to Kiev to say goodbye to her brother, who was moving to Israel. In the center of the country’s capital she saw graffiti on a wall that read, in large letters: “Let’s drown Russians in Jewish blood.”

She and her husband, Victor, 73, survived Hitler and Stalin, tough postwar years and the challenges of perestroika. In the early 1990s, they faced the consequences of the Soviet Union’s collapse and the birth of post-Soviet Ukraine.

“I’m Jewish, and my husband is Russian,” Ms. Shchetinina said with a heavy accent, carefully choosing words from her rudimentary English vocabulary. “We both felt unwanted.”...