Does a user converted to a shared mailbox still require an AD account.

As part of our process for handling mailboxes for terminated users, we are converting the users' mailboxes to a shared mailbox and assigning the appropriate member(s) access to the shared mailbox.  As it stands, we have a lot of stale users in our on-prem AD infrastructure, as the terminated users are just disabled and moved to a different OU.  I am wondering if after the mailboxes are converted to a shared  mailbox, does the AD account need to remain in order to retain all the previous emails in the shared mailbox.  If it's not as simple as just deleting the old users after converting their mailbox to a shared mailbox, is there a different process to keep the AD clean of disabled users, while retaining their mail?  Downloading and retaining the .PST files is not a viable solution for our company, so I've already ruled that out.