There is avast spectrum for empathy. A lot of people even NORMs have some trouble with empathy, for others with some disorders even more trouble with empathy. Some claim they can turn it off or on, there is no reason to doubt that because we are talking about a wide spectrum here.

The definition of empathy is it is made up of two parts to equal true empathy.
Cognitive: the ability to understand it, and affective: the ability to actually feel how the other person feels. Most ASPD and NARCS have cognitive, as do most people. It's simply the intelligence to recognize some one is in pain and understand why they are in pain.

So it's very possible if this two part theory is correct for any one to have a problem with either components or both to no fault of their own. A person with very good cognitive can even simulate the feeling without actually feeling it, if they wanted too. And many ASPD will do that for their children or some times spouse. Caring is a option.

Forget Freud. We've made huge advances since his "Book of Dreams". Recent studies suggest there are actually 2 sub-levels if sociopaths. And the second sub-level is believed to feel some empathy. Also interesting according to the DSM5 they now add trouble with empathy with borderlines, joining ASPD and NPD.

Personally I believe any thing is possible, the key for sociopaths will center around bonding. If they can bond to some one it opens the path for conscience and empathy.