Java - Log4j2 ErrorHandler not handling exceptions

I wrote a custom ErrorHandler that should shutdown the application if the logger is not able to log to its logfile.

import org.apache.logging.log4j.core.ErrorHandler;

public class LogFileErrorHandler extends ErrorHandler {
   private static final Logger LOGGER = StatusLogger.getLogger();

   @Override
   public void error(String msg) {
      LOGGER.error(msg);

      System.exit(ExitCodes.IO_LOGGER_COULD_NOT_WRITE);
   }

   ... more error implementations
}

Apparently there is no easy way to add it using the configuration programmatically.

Therefor I wrote this code as a workaround to add the ErrorHandler to my Appenders. It works and I can see that the ErrorHandler is added to my Appenders.

public void addErrorHandler() {
   final LoggerContext context = (LoggerContext) LogManager.getContext();

   for(Appender a : context.getConfiguration().getAppenders().values()) {
      a.stop();
      a.setHandler(new LogFileErrorHandler());
      a.start();  
   }
}

I had to stop the appender before adding the ErrorHandler because otherwise I got the exception:

The handler cannot be changed once the appender is started

My question

I did a test where I locked the logfile in order to produce an IOException (Access denied). For some reason the Exception was handled by the DefaultErrorHandler instead of the custom one that I added.

Why is the exception not handled by my custom ErrorHandler?