An E_CORE_ERROR is a fetal error that will end execution of your script.
Core errors are caused by PHP's core, and will not by thrown by functions. Very few things seem to cause core errors.
E_CORE_ERROR is included in E_ALL., and will not be sent to a custom error handler. Instead it is handled in accordance with the error_reporting setting.
To show all errors:
Here is a few examples of potential core errors:
Arrived at end of main loop which shouldn't happen
Attempt to destruct pending exception
Internal zval's can't be arrays, objects, resources or reference
Couldn't find implementation for function