Congenital insensitivity to pain is a rare condition where a person cannot feel pain (physical). Is there any condition relates to emotional pain or any pain not related to physical that a person cannot feel?
There are certain conditions in which a person may not be able to feel certain types of emotions, such as in psychopathy and related anti-social personality disorder. This may be related to abnormalities in the limbic system - an area of the brain associated with processing emotion.
However, it is not always clear whether or not individuals who appear to lack the ability to feel certain types of psychological pain (eg, PTSD) in fact cannot feel it, or they can feel it but are indifferent to it, as in emotional numbness or apathy.
Additionally, modern theories of emotion suggest that emotion is "subjective" (context-dependent) - that is, physiological aspects of emotion (such as pain) are only part of the picture, and many other cognitive factors come into play. So for example, in the case of a broken heart, as with psychological pain in general, it appears to share some mechanisms with physical pain - ie, this type of pain is effectively the same as physical pain. Nonetheless, CIP patients appear to be able to feel emotions such as heartache normally, suggesting that the mechanism is much more complex, and physical pain is neither necessary nor sufficient for feeling psychological pain. The added complexity may be the reason why an emotional analogue to CIP is not known - the number of systems that would need to malfunction simultaneously is too unlikely. It is also probable that given the importance of emotion to normal functioning, that a condition of not feeling it would be equivalent to death.
PS: Sorry that I don't have any book recommendations for you, but Wikipedia articles I linked to contain many references to literature you can check out.