Many organizations have asked for this kind of status for situations like large, public contests. Often, the winners are "Accepted" within Submittable, a public announcement is posted online, and the organization does not want to "Decline" all of the remaining submissions, but would like to mark them as having been "Completed".
You can update the status of any submission to "Completed" in exactly the same way as "Accepted" and "Declined":
From the submission list, select some submissions and click the dark blue "Mark as Completed" button:
Or, from the details view, use the option in the submission status dropdown menu:
Then, fill out the response in the same way as when you accept or decline a submission. You can select any "Other" response template, or enter your own response in the area provided.