When you say a system error occurs. What exception? Is it the FinderException? How do I catch it? Or do I not need to?
A system exception is defined in the EJB spec an an exception which the client does not expect, and is either a RuntimeException or a RemoteException. It won't be a FinderException as this is an application exception, ie a checked exception which is expected by the client.
(As a general rule, do not handle system exceptions in your bean code, just duck them to the Container. If you insist on handling these exceptions, make sure you rethrow them.)
Let's say that you had a connection but it's gone down. When the container discovers this and can't reestablish the connection, it may throw a system exception. This exception will be either a RemoteException (for a remote client) or an EJBException (for a local client). EJBException is a subclass of RuntimeException. Note that sometimes the container will throw a subclass of RuntimeException or EJBException. So, you may need to code your client to handle the subclassed exceptions.
Or your bean code will receive an SQLException. In this case, you will want to wrap and rethrow it as an EJBException.