In an internal memo sent this week, Apple announced that customers who've had an iPhone or Mac repaired by the Apple Store or an Authorized Service Provider are now eligible to purchase AppleCare+, as long as their device is less than a year old and it passes inspection and diagnostics.
An example scenario: A customer named John purchases a new iPhone, but he decides not to pay for AppleCare+ coverage for the device. A few months later, John drops the iPhone and the display is cracked. John takes the iPhone to an Apple Store to be repaired and faces costly out-of-warranty service fees since he decided not to purchase AppleCare+. Since the iPhone is less than one year old, John is advised that he can still purchase AppleCare+ for the device so that any subsequent repairs aren't as expensive.
Customers are still required to pay Apple's full out-of-warranty fees for any repairs completed prior to purchasing AppleCare+ coverage for their device.
More details on AppleCare+ can be found here.