CloneNotSupportedException in Java is an exception that occurs when the clone() method is called on an object whose class does not implement the Cloneable interface, which is necessary to legally clone an object. Classes should implement the Cloneable marker interface and override the protected Object.clone() method with a public method to avoid this exception. An example illustrating this exception involves a Person class that attempts to clone an object without implementing Cloneable, resulting in CloneNotSupportedException. To handle this, the Person class is updated to implement Cloneable, allowing cloning to proceed without error. Additionally, tools like Rollbar can help manage and analyze such exceptions in real-time, enhancing confidence in deploying production code by automating error monitoring and triaging.