Inbox messages are different from most other campaign types in that they sit in a customers inbox on your site or App and contain the feed of content that has been sent to it for each user. If this content is time sensitive for example an event related message or a time limited offer then you set it to expire at a relevant time when creating the campaign.
To allow you to see what Inbox Messages are live in the wild we created the Inbox feed page. To find this page navigate to Campaigns > Inbox Feed. You will see active messages and expired messages you can expire an active message like an out of date offer with the stop button.
If you want to expire messages on a one to one basis there is an API method to do that. This could be integrated with your CRM for example to remove an offer after a user has redeemed it. Details on that in docs here: