What happens to en route flights when a major earthquake etc. destroys facilities? Suppose you're flying a big plane in to an airport like Mexico City, already in final descent, when an earthquake strikes.  Large cracks appear in the paved infrastructure catching some vehicles by surprise.  The airport suspends operations.  Planes planning to take off are stuck on the tarmac for at least several hours. 
Planes planning to come in from farther away are told not to, maybe from an external seismic monitoring service if communications are out.  Those already in the air but far enough away to be able to divert can land at other airports.  

Yesterday, the main infrastructure was inspected and found to be OK, and the airport reopened several hours later.  But what would have happened if the earthquake had been strong enough to destroy the runway or other landing-critical infrastructure at this airport and at the nearest alternative, so that neither "rack &amp; stack holding patterns" nor "just go to the alternate" (as in e.g. a terrorist takeover at one airport) are viable options?  Are there special rules/considerations in place to help protect safety in such a rare region-affecting event?  

Continuing the distinguishing analogy from the terrorist takeover question, this situation is more like a widespread cyber-attack, solar flare, or electromagnetic pulse that knocks out ground facilities and prevents landing at multiple airports without destroying in-air flights in a way that e.g. a sudden volcanic eruption or nuclear explosion might. This question also focuses on emergencies that arise quickly and without the kind of notice that would permit a planned closure (as e.g. a hurricane would).
This is a valid and good question. The answer is all the different entities will work together to solve the issue.

It's called a system wide event, be it a natural disaster or otherwise.


  [It's an] event that affects a flight and a sufficiently wide area that all alternate routes and airfields briefed during pre-flight preparation have become unavailable. Ground facilities such as navigation beacons and air traffic services may also be affected.


A somewhat recent example is the closure of many airports in Japan after the 2011 Tōhoku earthquake and tsunami.

As you can imagine, this only affects a tiny portion of flights that are too near the center of the event. The ATC, flight-crew, and company (airline) personnel will all work together. Even a simple thing such as using the internet access aboard planes to gauge the situation on ground from the different news feeds can be used.

Best case scenario is there would be enough fuel to turn around and exit the radius/area of the event toward the most suitable location. There usually will be enough fuel, and using the performance manuals the flight crew can make their plane very efficient. Airlines balance fuel and time using what's called a Cost Index, in this case, they will push to save on fuel and forget time (flying slower but farther).

In conclusion, the affected are few, the events are far between, each flight will be very unique, and this is where human ingenuity, training, and decision making skills come in.

For the facilities part, there are a few posts on that here, for example see: Is there an ATC radio backup? Even if the radio is down, handheld radios can be used. Most of the aviation systems have many built-in redundancies.