If the the account had been set to use POP, or if you had stored messages in Local Folders, then you actually have local copies on your computer which are yours to keep. If the account used IMAP then what is happening now is a happy accident. Move those messages to Local Folders ASAP if you want to keep them. Personally if I had a "dead" account I'd want to be rid of it. Inevitably at some point it would try to connect to the server and generate error messages when that failed. So I'd move the contents to another account, or Local Folders, then remove the account. See the common thread here? Local Folders is the answer every time.