Assata Shakur escaped from a U.S. prison in 1979 where she was serving a life sentence for the killing of a New Jersey state trooper. Members of the Black Liberation Army broke into Clinton Correction Facility disguised as visitors, took guards hostage, and used a prison van to facilitate her escape. After her escape, she vanished and later resurfaced in Cuba in 1984. The Cuban government, under Fidel Castro, granted her political asylum that same year. This asylum was part of Cuba's support for revolutionary movements opposing the U.S. capitalist system. She remained in Cuba for the rest of her life despite U.S. efforts to have her extradited.

In summary, Assata Shakur got to Cuba after a dramatic prison escape in 1979, followed by clandestine travel that ultimately led to her asylum in Cuba in 1984.