Sitemaps for jobs

For the job site builders… Do you keep closed jobs in your sitemap or only pull in active jobs?

Keep the page, remove the apply button if any, also set the the jobPosting schema validThrough property in the past.

Also I reckon the Google Indexing API for jobPosting…

For SEO, you could change it to an archive, or link to related or new jobs.
Or a form with 'alert me' if there is a similar job available.