When an iOS application goes to the background, are lengthy tasks paused?

From the iOS App Programming Guide:

Your app delegate’s applicationDidEnterBackground: method has approximately 5 seconds to finish any tasks and return. In practice, this method should return as quickly as possible. If the method does not return before time runs out, your app is killed and purged from memory. If you still need more time to perform tasks, call the beginBackgroundTaskWithExpirationHandler: method to request background execution time and then start any long-running tasks in a secondary thread. Regardless of whether you start any background tasks, the applicationDidEnterBackground: method must still exit within 5 seconds.

If the long-running operation you describe above is on the main thread and it takes longer than 5 seconds to finish after your application heads to the background, your application will be killed. The main thread will be blocked and you won't have a chance to return from -applicationDidEnterBackground: in time.

If your task is running on a background thread (and it really should be, if it's taking long to execute), that thread appears to be paused if the application returns from -applicationDidEnterBackground: (according to the discussion in this answer). It will be resumed when the application is brought back to the foreground.

However, in the latter case you should still be prepared for your application to be terminated at any time while it's in the background by cleaning things up on your way to the background.

If you are doing some operation which might consume time and you don't want to kill it then you can extend the time for your operation by executing in UIBackground Task i

{
    UIBackgroundTaskIdentifier  taskId = 0;
    taskId = [application beginBackgroundTaskWithExpirationHandler:^{
        taskId = UIBackgroundTaskInvalid;
    }];

// Execute long process. This process will have 10 mins even if your app goes in background mode.

}

The block argument called "handler" is what will happen when the background task expire (10min). Here is a link to the documentation