Hello @jragregorio ,
If you are using Jira Datacenter, there is a project archiving function. If you are using Server / Cloud, you can refer to the suggestions in the following posts.
Think before what you are doing !
Some links in the instance will break as this is mentioned in some of the XML files.
If you want to hide the projects there are number of ways,
In Data Center, there is option available to archive projects and also each issue.
In Server, you need to remove all Permissions in the Permission Scheme.
As in Cloud mentioned by @Ollie Guan_携程 Follow the links
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