From the Case Summary: "Atanas Entchev (“Entchev”) entered the United States in August 1991 as a nonimmigrant exchange visitor on a J-1 visa. His wife, Mayia Entcheva, and son, Enislav Entchev, entered the United States in 1992 and 1993, respectively. They were authorized to remain in the United States until July 30, 1993. Before their authorization expired, the petitioners applied for asylum. Entchev argued persecution based on his political beliefs in opposition to the Communist party, which ruled Bulgaria until 1989."

So they applied for asylum on political grounds in 1993, because the Communist party was dethroned 4 years earlier. Well...