Anomalies and signature PVE sites in wspace move from system to system when they despawn. The most obvious way they despawn is when you run them to completion. One of the subgroups of the final wave is the trigger for the despawn event. As soon as you kill that group, the site will be removed from the discovery scanner system. However, the on-grid elements (sleeper structures and any remaining sleepers) will remain until all players have left the grid for a short while.
Sites also despawn based on being around too long. Sites despawn on the fourth downtime once they are triggered. ("Triggering" a site, or "activating" it, happens when you warp to it. You don't actually have to warp, just to start it; you can cancel.) I have read that sites will despawn eventually even if not triggered. However, I am skeptical of this. The duration I have read somewhere for this is a week. Certainly, a week is contradicted by observations; see below.
One of the consequences of the way sites despawn is that they will naturally spawn into a system based on the rate they are being run overall at that level. Thus, when I lived in C1, I observed that we would get perhaps one or two new sites per week on average. This is because few people run C1 sites. C1 sites are worth doing, but most people who live in C1 don't bother. In C4, sites spawn more quickly. We get on average perhaps one new site per day. This, combined with the average site value of perhaps 80m ISK, is enough to provide a small corporation a decent income.
Another interesting aspect of the system is that sites tend to pile up in systems where nobody lives, or where the locals don't run them. In C4 the sites are worth running, and it appears that most groups do run their local sites. But there are still many empty systems. These tend to pile up sites, becoming site "graveyards" as I sometime call them. I explore a lot as a part of hunting. I frequently see systems with 40+ sites, almost always unoccupied. Indeed, finding more than about 20 sites is a pretty reliable sign that a system is not taken. (You should still warp around to be sure.)
I recently ran across a system that has the most sites I have ever seen. It had 19 signatures, and 69 anomalies. You can see them here:
One interesting thing about graveyards is that we can use them to get a ballpark figure on how likely it is that sites do eventually despawn on their own. If we get one C4 site per day on average, and sites despawn in a week, we should expect a C4 graveyard to hold just seven sites. It would hold more if it was lucky, but the odds of any system holding 88 sites are astronomically low. 88 is high, but not that much higher than other systems I have seen. Estimating one new site per day, and if sites never despawn except via timeout, we'd expect 88 sites as a steady state if sites last 87 days on average. Since the system is unusual the real figure should be less, but not that much. Perhaps 60 days. If two sites a day is average, then the timeout value is around half as much.
My gut feeling is that sites don't despawn on their own. Players do run them eventually, even in black holes, or else they trigger them.
After scanning down the system, I grabbed the screenies above. First I activated all of the sites, though, according to my standard operating procedure. Here's how the system looked on the system map:
That was August 16th. If you live in C4 and got a new site on the 20th, you're welcome. If you live in C4, please pitch in to the common good of C4 and always activate all the sites in C4s you connect to.