Set up a new read-only Stack Exchange site on a new domain. On request and at their discretion, moderators could undelete questions and migrate them to the new site. (Users are redirected to the new site if they visit a question that was migrated there from another site.)

Exclude the site and its posts/activity from most of the listings and indexes on the rest of the network, to emphasize that this content has been removed from the Stack Exchange network. Include a disclaimer in the header of every page.