Suppose 'the worst' happens. Stack Exchange folds (commerical entities have been known to), and at the same time the moderators lose all interest and/or decide the despise mathematics. Where would this leave us?

People are citing MathOverflow in many published papers, so it seems we have some obligation to attempt to ensure that the content remains accessible forever.

Public dumps exist (although they are up to 3 months), and it's likely that someone would have retained a copy, even if the site they are currently served from became inaccessible. From this dump it would be relatively easy to create a read-only website containing the contents of MO, and if one could obtain ownership of the domain name (which is owned by the MathOverflow corporation, not StackExchange) it would be relatively easy to have all the links from the literature resolve to the correct (but read-only) places.

Is there something else we can do to ensure the long-term archiving of MathOverflow?

Are there libraries that would be interested? The Internet archive? The arXiv itself?

It would be relatively easy to produce a giant PDF snapshot of MO (e.g. I know how to script creating PDFs from webpages, including rendered MathJax). The question becomes whether anyone really reliable would want to take them.