More likely Hainan, as others suggested, or if you wanted a true analogue to Taiwan (exile territory on the periphery of Chinese empire), have the CCP, its personnel, and 1-3 million hangers-on escape to Outer Mongolia after losing the civil war, which for years afterward still sees occasional forays by the communist forces into Inner Mongolia, Xinjiang, and Manchuria. The ROC claims Outer Mongolia as a rightful part of China, while the Soviet Union quietly drops its recognition of an independent Mongolia in the mid-50s and to Mao's annoyance, does not recognize his People's Republic, but regards CCP-held territory as merely the "liberated zone" of the ROC.
For the first half of the Cold War, the PRC remains a thorn in the KMT's side, with the long border being a source of spies, terrorism, and arms trafficking to restive parts of the ROC. This lessens greatly after Mao's death, with the post-Mao leadership using the detente thaw to improve relations with Nanjing. After the fall of the Soviet Union, the PRC faces imminent economic collapse, and Mongolia is peacefully reunified with China proper; in exchange, the CCP leadership is spared treason and sedition charges.