Take a look at the iOS Application States.

applicationWillTerminate: looks like the obvious choice but it is not guaranteed to be sent to applications which run in the background. Your best bet would be applicationDidEnterBackground:

Basically, when your app is backgrounded, write out that it is in the background state. When it is foregrounded, write out that it is in the foreground state. When your app launches, check whether the background flag is set - if so, the app was killed while in the background - either by the os, the user, or lack of power. It's not ideal, but is the best you can do on an iOS device - since an application can go from "not running" to "terminated" without executing any code, you can only rely on background / foreground.

You should get applicationDidEnterBackground: called for every situation except for sudden power loss / destruction.

Just adding onto turch's suggestion,

Try keeping the game's data file open during play and writing small bits of data into it periodically. You can probably do this at run-time without too much of a performance hit if you make sure there is an appropriately sized buffer. This will also allow you to do any pre-termination cleanup quickly because you are not writing out to the whole file, at once, just before the OS kills your app.

You would also want to do a quick integrity check of the data when first loading it and have it backed up for the worst case scenarios.

Yeah Demon Souls and Dark Souls do this as well.

If you are comfortable enough with multi-threading you might want to look into that. Just have a separate thread constantly checking for changes in the game and then saving the important ones to some file. You can have whatever threshold you want to determine if this is important to the game; remember the player doesn't always have to be brought back right to where they left off. As long as the variables that are most important have been saved you can just send them back to the last known checkpoint or however your progression system has been setup. This way you are not constantly writing to some file your latest position data every frame.