Depends a lot on the game in particular.
For instance in an rts you never really want game objects to stop updating because a key part of an rts is that units will always be under the implication of something might be happening to them, your band of warriors across the map might be getting attacked by ghosts while your camera is at your main base clicking create units.
In a game like skyrim you have different states objects may be in depending on distance and such. For instance when you're out in the world map the game world is split into cells, cells are loaded and unloaded based on distance around your character. However you still need to render things like the terrain, and distant mountains, the game has a system where it renders the terrain at low detail level depending on your distance to it and it starts to load and change the asset quality as you get closer, when you move a certain distance from a cell it will also unload the entities in it(small detail objects like rocks and plants and things) essentially a lot of game cells will be "dead" at any given time, as in they won't be updating any objects in them, just rendering the basics of the height map and certain large objects.
For things like the ai I'm not entirely sure how skyrim does it despite the fact I play it a lot. In oblivion they tried to sort of "patent" a new system of ai where every npc had a set routine based on time, they modified that a bit because it was really robotic always seeing the SAME conversation happen at the same exact clock time in game. My assumption based on that, is that when you enter an unloaded cell like a town it probably loads the entities and then simulates their behavior, a lot of this might be trickery and assumption. For instance a shop might restock itself automagically just as a product of time having passed. Npcs migh be moved depending on the current clock time, some randomization factor and their "schedule" so it looks like they were going about their business before you walked in, but they may not have been. They might even continue doing this behavio if you leave town but are nearby still to add a bit more realism to their movements if you enter the town again. These are all mainly guesses, but are ways you could handle it.
Using LOD and unloading chunks like that also happens in other open world games like farcry, the real meat of the behavior is based on the fact the player needs to be able to see distant things like terrain and large structures but it would be a total waste to be updating objects or actors in these far off areas if you are nowhere near them. Thats the trick of it, and that varies wildly from game to game. On some game types areas may always need to be loaded, in others they might be completely unloaded. Something like minecraft for example, when it unloads a chunk it flat out removes it and stops drawing it.
Explaining the rendering is a bit of a large topic for one thread, a lot of how to remove excess geometry in rendering depends on what tools you have for subdividing the game world(is the map split into chunks? can you use the position of the camera to cause certain areas to not be set to render?) Its a case by case thing.
Edited by Satharis, 03 April 2014 - 08:33 PM.