In JAX-WS, a Java exception thrown from a web service is mapped to SOAP fault when the XML payload is sent to the client. On the client side, JAX-WS maps SOAP fault to either SOAPFaultException or to the application-specific exception. The client code could wrap the web service call in a try...catch block to handle exceptions thrown from the web service.
For a good description of how SOAP exceptions are handled in JAX-WS, refer to https://docs.oracle.com/cd/E24329_01/web.1211/e24965/faults.htm#WSADV624.