Maybe I'm saying something stupid, but couldn't the pirate bay be distributed as a torrent that is continually updated, and then you have a torrent client that can search the database?
In fact TPB was already not serving torrent files in large part; every torrent with more than a handful of peers is stored as a magnet link, which literally is just a content hash. I'm positive there's something rather clever to be done there, but we can't put it into a torrent.
The javascript fires off, accesses a torrent (hard-coded into the html itself), which loads content for the website... images, js files, everything. It also loads the data (I'm assuming it's small, but I've read claims that the data is only about 90 megs) into javascript storage, ready to be searched locally.
The torrent swarm itself could become so big that it'd be self-sustaining, no original seeders would need to stay online vulnerable to legal threats.
To have the torrent continually update with new content, you'd have to break the protocol (which, for this one purpose, might not be bad). But I don't understand it well enough to know this is even possible for certain. With magnet links, you first have to download the whole torrent file before you can start downloading, and it may not be possible to coax it into get the updated torrent file again.
Even if you can't do that, updates themselves might just be new torrents... we can run javascript on this page, so we can be clever and have it derive new torrents/hashes to download. It would be good if anyone could update the data, for instance, adding torrents (though how to police that so they don't add junk or poison the thing... not sure).
A system like Bitcoin+BitTorrent could do what you're describing, with Bitcoin filling in the missing distributed hash identification function. I don't really follow the distributed web scene, but I'm sure that's an area of active research.
It's a combination of people who have read-write access and people who have read only access but still contribute to the swarm. I think it's got potential.