I am using a design system within an organization, but the organization want us to move the project out of the organization. I think this could also be a case when an organization want to share their design system with the community and let everyone take advantage of it.
No, you can’t. @miggi can you confirm ?
Depends on how it is set up, what you are sharing outside of the org and the dependencies. If you have one file with all of the main components and everything is spread across pages without dependencies—publishing those as community files will give someone the ability to duplicate and set it up as a library in their own team, but things like shared styles from libraries will break.
Here is an example of how Shopify is sharing its system publicly: Figma - @Shopify. If you duplicate one of the Shopify files, the colors styles may be identified under selection colors, but you will not be able to change them out as if they were published styles like you would within the org.
There may be other org-level ways of transferring teams and libraries, but I believe that may require contacting support. This I am less familiar with.