In some scenarios, we want the process continuously executes the further steps and ignore the error. In Java code, it is pretty easy and what you need to do just uses a try..catch and then properly set the variables and not throw the exception again. In OSB, it has a little bit difference and a Resume action must be introduced to make the process resumed and executed continuously to handle the further steps.
If neither the Reply nor the Resume action is initiated, the error is rethrown. In this case, the error is pushed forward and handled by the next level error handler. Unless otherwise specified, the rethrow action is the default action of an error handler.