I created an online account on a website, they do not ask me for a password but just an email address, then, after acknowledging "terms of service" I was already logged-in.
Then I received an email with a password (ten characters like automatically generated password) and this advice:
Please note that passwords are case sensitive. [website name] handles sensitive information on behalf of some its members and other organisations. To help protect your data, we automatically assign secure passwords. To maintain this security, you cannot change your password and we have no means of retrieving lost passwords.
This was something I have never seen before and leave me with a lot of doubts about the trustworthiness of the website. I was expecting at least the capability to change the password.
update with more details: I did not realize immediately I was already logged-in and so I mistakenly logged out, but I was obviously without a password, so I clicked on their "forgot password" and then I had a look at my incoming emails: an older welcome email with the first password and a second newer email due to "forgot password". The password of the older email is working, the password of the newer email does not work. After all, they wrote
we have no means of retrieving lost passwords.
And they also add:
Please make sure you do not share your password with anyone. We recommend that provided you use a recent browser, you use your web browser's "remember password" function to provide ease of access while retaining password security.