An error triggered in the exception handler can be handled in the shutdown function using error_get_last(), that error will be taken as a fatal error no matter what level it is originally of.

If an exception is thrown in the exception handler, the exception will NOT be handled by the exception handler, instead it will be converted to a fatal error that can be handled by the shutdown function.

As of PHP 8.3, an exception thrown in the shutdown function can be caught and handled by the global exception handler.