Strangely, Java Doc says:
These methods are designed to be used as tools for creating higher-level synchronization utilities, and are not in themselves useful for most concurrency control applications.
Is there any example/scenario to illustrate JavaSupport is useful?
It's used by many classes in the java.util.concurrent package, as explained in the Javadoc. You're not supposed to (or rather you don't need to) use it unless you're creating your own high-level concurrency classes, since there are plenty of ready easy-to-use classes that can accomplish what you want, without going down to the "bare metal".