Hi! I was mistaken in my earlier response. The core plugin *will* show filled jobs on the [jobs] page. By default, it does so by changing the text colour so that it looks unavailable. If you click through to the job, it will show “This position has been filled”.
On the Jobs Dashboard itself, you can mark positions as filled:
https://wpjobmanager.com/document/the-job-dashboard/
Your original question was:
Our Job listings are not showing a check box for whether a position is filled. Does this have to be added?
If you want a checkbox to show to site visitors that the job is filled, this is dependant on your theme; you can likely add one via CSS. Am I understanding your question correctly?