RE: Real Time Example for "Final" keyword used in X++ Class
I can easily find hundred examples, but you can do it by yourself, so I won't waste my time with it. But will hundred examples help you more than the single example I already gave you? I doubt so - I think what you need is understanding why developers want allowing other people to inherit from a class, or when they want to prevent it.
In some cases, you want other people to create specialization of your class, such as when you can create custom classes inherited from RunBase. In other cases, you want to prevent it. I already mentioned one such situation - if extending a class makes no sense, any such any attempt would be a bug. If the class is final, anybody making such a mistake will get an error at compile time, making clear that it's not a valid scenario. Or you may want to be sure that nobody meddles with the critical piece of logic that your class performs, you don't have to design the class to be meaningfully extensible (e.g. which methods will be protected and which ones private), there are performance benefits of final classes and so on.
Note this topic isn't specific to Dynamics AX; it's about object-oriented development in general, so you can consult books written for other languages as well (such as Thinking in Java).