If this is a POP account, the messages will remain. If an IMAP account, I encourage you to COPY (not move) all messages to Local Folders before closing the account.

Thanks David how do I copy all messages to a local folder?

First, make sure you have all the messages. clicking File>offline>download should do that Then, a clean way is this: - click help>troubleshootinginformation - scroll to 'profile folder' and click 'open folder' - EXIT thunderbird now - you are now in windows file explorer - your account is at imapmail\<IMAPaccount> messages are there, such as input, input.msf, sent, sent.msf - the Local Folders folder is at Mail\Local Folders - Click to the Imapmail\<imapaccount? folder in that folder and COPY the folders other than the msf entries and paste into the Mail\Local Folders folder. - restart thunderbird and the messages should be there </p>

david thanks again. I tried following your instru but when I open profile it only shows imapmail not imapmail\<IMAPaccount. Can I use sync & storage to advanced and items for offline use. Where does that file go. Also when I can windstream what is used for my email on thunderbird? Sorry for all the questions I am not a good computer person </p>