VANCOUVER, Wash. — Growing up in the 1970s and ’80s in Ukraine, then part of the Soviet Union, Halyna Davydyuk was bullied by classmates and by teachers, who forced her to sit in the last row because she was an evangelical Christian. Her father was jailed for his beliefs.

Today, she said, “there’s not a lot of persecution, but it’s difficult to find work.”

Normally, someone seeking better prospects in the United States would wait several years to be admitted. But Ms. Davydyuk, her husband, their seven children and a daughter-in-law arrived here in Vancouver in May just two years after applying. They joined a growing number of Ukrainians who have streamed into the United States in recent months even as the country has closed the door on other refugees.

What distinguishes the Davydyuks, who are Pentecostal, from other immigrants is a program created nearly three decades ago to benefit those who suffered from religious persecution in the Soviet Union, where the Communist Party hounded religious groups it could not control.

There is far more religious freedom in their countries now. But while refugee camps in several continents swell with families escaping Islamic fundamentalists and bloody civil war, the ex-Soviets still enjoy a favored status when applying to come to the United States.