The Soviet Union basically cut off support for Cuba at the end of the Cold War.
Early 2000s American newspapers had articles about the practice of breeding and training oxen being revived in Cuba, because Cuba was no longer receiving subsidized oil from Russia and Azerbaijan. Economically, male oxen are like mules -- they require a substantial investment, and do not reproduce.
What Cuba had provided to the Soviet Union in exchange for cheap oil (and other support) was soldiers and leaders for revolutionary movements in many third-world countries, and a conduit for providing Soviet support to those movements. For example, El Salvador, Nicaragua, Angola, and other countries. As mentioned in the original post, at the end of the Cold War, the Soviet Union stopped supporting these causes, so Cuba's help was no longer valued.
Since Hugo Chávez came to power in Venezuela, Cuba has provided leaders, teachers, and inspiration to Chávez' party, and Venezuela has provided subsidized oil to Cuba.
This 2009 AP article (via NBC News) mentions both Cuba's use of oxen and the Venezuelan oil subsidy. This 2017 OilPrice.com article says that Cuba has received substantial amounts of oil from Venezuela since 2000, but that there was an 8-month "hiatus" in 2016-2017. It also says that Cuba did not receive any oil from Russia after the end of the Cold War, but has started receiving oil from Russia as of May 2017.