I know some email services that encrypt incoming email. You upload your public PGP key, and when an email arrives, they encrypt it and then store it using your public key. It works like the sender uses PGP, but then at a later stage. When you download the mail via POP3 or IMAP, you need your private PGP key to decrypt the mail. Without your private key, the mail is lost.
Of course before the encryption has been done, and the original email has been properly deleted, everything is the same as with normal email.
As a side note: I've heard people state that their work email was "safe". This was in the health care business. Then they're probably talking about a web based system for taking notes, keeping records of clients, and clients get a login and can send messages inside the system. How safe is that? I can't tell, but probably safer than the average Joe User with no idea about safety handling his own email and antivirus.