How can I allow a user to send private messages but prevent other users from sending that user a private message?
There are two ways to do this.


The pm_block_user module has settings that allow for role-based configurations for who is allowed to write whom. However, it is only possible to add positive rules. Meaning, you wold need to add all your users into a normal role that the system user is not part of and then allow users of that role to write users of that role.
Implement hook_privatemsg_block_message() and block the system user id.


You're welcome to provide option two as a patch in the main module (e.g. allow to choose a system user whom you can't write/reply and is maybe also themed differently). This is an often requested feature.