what happens if your business exception extends Runtime Exception

Any exception with runtime exception is an unchecked exception hence we don't need to check it and will be handled on its own! Primarily, any exception whose handling costs seems to be too much should be be an unchecked exception.

it will throw the runtime exception.

It is not recommanded because business exception should be caught in compile time instead of run time.

Extending the Runtime Exception means you are giving the definition of your exception as System Exception, for each System Exception your container will do a different process, mean what ever transaction you have, would be rolled back and the instance of the current stateless would be destroyed. If you are using a Stateless bean, you will not get too much of effect apart from an exception, but in case of Statefull your bean will no longer be available to serve your other request in same session.