I'd recommend writing a custom handler and log within, e.g.
[AttributeUsage(AttributeTargets.All, Inherited = true)]
public class HandleErrorAttributeCustom : HandleErrorAttribute
{
public override void OnException(ExceptionContext context)
{
base.OnException(context);
log4net.LogManager
.GetLogger(System.Reflection.MethodBase.GetCurrentMethod().DeclaringType)
.Fatal("Not captured exception", context.Exception);
}
}