All sites that viewed an existing site contain a copy of it and share the data. There is a "thundering herd" problem of multiple requesters for the site initially being distributed but once that's done then multiple nodes will have it and can seed it. The original site shutting down is no problem at that point.

IPFS shares the same problem and knowing when it's safe to shut down a node in both IPFS and ZeroNet is difficult.

Freenet solves this by having an insert of data sent directly to peers immediately. The site isn't stored on the inserting node. Once the insert is done it's safe to close the node and the content is still available.