Anatoly Kurmanaev, Wall Street Journal
Photo Credit: Diana Zeyneb Alhindawi/WSJ

CIENFUEGOS, Cuba—Fidel Castro and Hugo Chávez proclaimed a decade ago that they presided over a single country, combining Cuba’s educated workforce with Venezuela’s oil wealth to challenge U.S. power across Latin America.

Now Mr. Castro is gone, three years after Mr. Chávez’s death, and the union between their two countries, while still strong on paper, is withering away fast.