The EmptyStackException in Java is a runtime exception thrown by Stack class methods to signal an attempt to access elements in an empty stack, as demonstrated by the Stack.pop() method causing this exception if used on an empty stack. Since it is an unchecked exception, it does not need to be declared in a method's throws clause. To prevent this exception, programmers can check if the stack is not empty using Stack's isEmpty() method before performing operations like pop or peek. Handling exceptions effectively is crucial for robust code deployment, and tools like Rollbar offer real-time error tracking, analysis, and management to streamline the process of fixing Java errors, enhancing confidence in deploying production code.