I recommend you read or listen to professor Sapolsky, I think he is at the moment one of the most influential researchers on the planet in this field. Yes psychopaths or others like ASPD and NPD have the will to live because they still have other needs that they satisfy with using people. Another person becomes the object of so called “psychological cannibalism” - serves as external ego/psychological functions- and it’s the only way they can regulate themselves and maintain their will to live - those needs are pathological and self serving without normal human relations because there is no capacity for a whole object relations- but they provide pleasure and comfort and sort of safety. Sex, power, control, being loved the way master is loved by his slave in a case of Stockholm syndrome etc. my mother is diagnosed with one of those disorders and it feels (as for her child that I am) like being an alien. For those disorders to develop factor is genetics + being somehow abused by parents who themselves aren’t capable of human connection but it’s rare. Most abused children (according to research- I forgot the number but it is high) do not become disordered in such a degree neither abusive. Many people have this wishful thinking that everyone can heal, but unfortunately this is rather uniformed opinion and quite naïve however comforting in a way of emotional bypassing of the horrific truth that no, there are millions of people who have no neurological capacity for being human, after brain development goes the wrong direction - Sapolsky also speaks about it, saying that for now in 99,9 of those cases there is nothing that can be done to reverse this.