This *already happens*. 

At the top of the [Artificial Intelligence Area51 page](http://area51.stackexchange.com/proposals/57719/artificial-intelligence) you see this banner:

> The AI site didn't have enough activity during the beta, and has been closed. You can download the [data dump of all questions here](http://sstatic.net/area51/datadumps/022014%20Artificial%20Intelligence.zip).

You can see this on [other](http://area51.stackexchange.com/proposals/11942/game-of-go) [long-closed](http://area51.stackexchange.com/proposals/164/firearms) [proposals](http://area51.stackexchange.com/proposals/3303/sexuality) [too](http://area51.stackexchange.com/proposals/6243/startup-business). 

Big Data is the *exception* here; I don't know why it doesn't have a data dump, perhaps it just had not generated enough data in it's mere 13 days of existence.