This may depend on your jurisdiction but I'm 99% sure this isn't how things work in Germany.
First of all, the author retains ownership of the copyright. They can freely redistribute copies of what they have written unless they're subject to an active contract limiting their use of those rights (e.g. a time-limited exclusive license -- IANAL but AIUI there is no such thing as a permanent exclusive license unless you also get perpetually reimbursed).
So if you're sent a copyrighted work by its author, you may legitimately infer that you have the right to access it but you don't have the right to republish it or make copies accessible in any commercial way (like an ad-sponsored online platform).
Additionally communications are subject to privacy laws. So you may be in violation of the author's personal rights even if you publish their e-mails non-commercially because you violate their "reasonable expectation of privacy".
This is not entirely dissimilar to the case of "revenge porn" by the way: if you send your loved one an intimate picture for private use, you can not only ask that they destroy the picture at any point but they are also prohibited from publishing it without your approval. Of course in this case the violation of personal rights also stems from the fact the photo is a depiction of the author.
But if you really need a clear example, imagine you are sent the draft of the next Game of Thrones season (or what have you) by its author. Unless you have explicit permission, you have no reason to assume you would then be allowed to go on and publish that document. Even without an NDA there's likely a "reasonable expectation" you will treat it as confidential and you'd be in violation of that by passing it on.
Note that I'm talking about my understanding of German (and likely by extension EU) laws, not necessarily American laws. I'm well aware the US has different laws and I suspect those might vary on state level too.