A "puppet state" refers to a country that is controlled by another country, like a puppet on a string. The controlling country makes most of the decisions and has significant influence over the puppet state's government and policies. Full definition
Petain rose in rank to eventually become Marshal of France and, later, Prime Minister of the Nazi puppet state, Vichy France. (businessinsider.com)
Nicaragua, nonaligned and successfully improving the living standards of the poor within the framework of a mixed economy and political pluralism, posed a far greater threat to U.S. interests than a Soviet puppet state ever could. (religion-online.org)
Japan would have created a malleable puppet state on Chinese territory, and would be able to turn its view towards other territories, Burma, Indonesia, perhaps even India and Australia, much sooner and much more easily. (blog.politics.ox.ac.uk)