My name is Jeff and I'm here to assist you. Let's work together in finding the right solution to this concern. I understand that some read emails in your inbox went missing.
You've mentioned that you're using Outlook for Mac 2011 as your mail client. Just to verify, is the account added in your Outlook for Mac 2011 a Microsoft account? If yes, please try to access your account through web browser in https://outlook.com and check if you can find your emails there.
Also, looking at the initial information you’ve provided, I can refer you to Microsoft Office for Mac to provide some clarity.