Yes this can happen. It's a sort of a race condition, for example when a mailbox is created for a user before the account is properly synchronized from AD.
The general method is to:
1. Copy everything you want to keep from the cloud mailbox to a PST.
2. In AD, move the user account to an OU that is not synchronized to the cloud.
3. Start an Azure AD Connect sync or wait for the next one.
4. When the mailbox disappears from the online EAC, remove the user account from the recycle bin in MSOL PowerShell:
Remove-MSOLUser -UserPrincipalName user@company.com -RemoveFromRecycleBin
5. In AD, move the user back to a synchronized OU.
6. Start an Azure AD Connect sync or wait for the next one.
Now you can move the mailbox to Exchange Online or leave it where it is, but it should be properly configured in the cloud as an on-premises mailbox. I'd recommend not applying an Exchange Online license if the user won't be needing one.
Ed Crowley MVP "There are seldom good technological solutions to behavioral problems."
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