A company hires maybe one or two new employees a year. Each job is posted in several external job-search listings, and given a page on the company website.
On the closing date, all links on the website to the the job posting are removed. The page remains on the site (including the closing date) and the only way to access it is if you already know the URL or search terms.
Should the posting stay up or come down? There is no standard established practice for the website.