note 9201 rejected from function.pg-errormessage by yohgaki

I am a native speaker. The manual page is grammatically incorrect and unclear. I think the author is trying to say that if an error causes the database connection to die, then you won't be able to get the error message. In such cases, you can at least infer the problem. The author may also be trying to say that if you get an error, then execute another database command, your error message will get lost. That would be a problem. In any case, it's clear that you can expect a string from this function if the last database command you sent resulted in an error.