CARACAS, Venezuela—“This is the first time I feel like an emigrant,” says Evelyn, who calls herself a “free spirit,” and whose name has been changed out of fear of retaliation. She has left Venezuela twice before. Now she is waiting in her sister’s apartment to be summoned for her final interview at the U.S. Embassy in Caracas to receive an immigrant visa and leave her homeland a third and likely final time. “Before, I escaped,” the 62-year-old consultant says about her prior adieus. “Now I am emigrating.”
There is singing in the next room. On the other side of a closed door, a group of women in their early 20s break into song. “So that she may never leave!” they repeat, joining Marc Anthony. In the song, called “Flor Pálida,” Anthony tells the story of a flower he finds in...