There are two points to make (a) in 2017, the South China tiger has been reclassified as the same species as the Bengal tiger (Panthera tigris tigris) and therefore technically we can’t discuss it as a species of wild cat anymore and (b) if the South China tiger exists as a species it is extinct in the wild. The last recorded individual was in 1970.
Mao Zedong, the famous leader of China, instigated the decimation of the tiger population in China when they were classified as ‘pests’ and slaughtered. The tiger in China was doomed to extinction through human neglect and indirect and direct abuse (loss of prey, hunted, loss of habitat etc..).
To recap: at late 2017, the are no South China tigers in the world in the wild and I don’t know of any in captivity which in any case is irrelevant as the South China tiger and the Bengal tiger are now one and the same species.
This sounds very strange but it is not because the classification of the species is in flux all the time. The IUCN Red List (the people who decide on population numbers) does not even list the South China tiger at the date of this post. However, it does list the Bengal tiger. I assume that this is because of the recent reclassification.
Classification carried out by: Kitchener, A.C.; Breitenmoser-Würsten, C.; Eizirik, E.; Gentry, A.; Werdelin, L.; Wilting, A. & Yamaguchi, N. (2017). “A revised taxonomy of the Felidae: The final report of the Cat Classification Task Force of the IUCN Cat Specialist Group” (PDF). Cat News. Special Issue 11. (From Wikipedia).