From Area 51 budding to public beta, there are many metrics like avg. traffic, activity etc which decide the fate of a SE site. But, what happens when a graduate SE site which was active for long suddenly becomes inactive? Would it be left as it is or would it be shut down?
I'm Grace Note, a Community Manager.
Nowadays, the entire point of the "graduation" stage in a site's lifecycle is to identify a site that has enough growing traffic and self-sustenance that it will not hit an "inactive" status. That's one reason why graduation is extremely infrequent even amongst sites that are "performing very well".
We on the Community Team are always watching every site. If we've done our job, then we'd never actually see a site one day just go dark, barring some kind of exceptional circumstance that we'd .. well .. need to deal with uniquely when it happened. Did a site just fall out of Google? Did some other site lure an entire community away? These are all exceptional scenarios for which no real policy can be prepared. I'd go further to say that because it'd be some extreme situation that would result in that kind of "death", we would have to evaluate these on a case-by-case basis, with our primary intention usually being the revival of the site. I do not imagine that there's likely to be any sort of consistent reasoning for this dropoff to happen repeatedly on the same reasons.
We also lack any mechanical systems for handling this kind of scenario. Since they hit graduation, it's a clear sign that there's enough value to the Internet as a whole that we can't just remove them in the same fashion as we handle Beta site elimination. But since this isn't a sort of situation we're expecting, we haven't delved into setting up any mechanism for publicly preserving their content.