Jira does not know a project status. There's an open ticket for that: https://jira.atlassian.com/browse/JRASERVER-1450
Maybe you want to vote for the issue.
There's a plugin "ictime time tracking" that offers some kind of project status, but it is not for free and I did not try that plugin, so I can't say, if it is worth the price. There may be other plugins, this is the first one, I found.
We "archive" closed projects by simply removing all the permissions on the project.
There's also an add-on that gives you "project fields" in the marketplace, you could use one of those for a status.
Most of us use a "closed" permission scheme (sometimes hiding the project, but usually just allowing read-only access so no-one can change anything), and often we use the project category to indicate groups of ended projects.
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