It's commonly believed that serial killers cannot stop, because their compulsion is so strong that they're literally addicted to murder. In addition, they feel no remorse so they have no reason to refrain from indulging their hunger for blood - or else they're just plain psychotic. In fact, to assist in the defense of Wayne Adam Ford, a psychiatrist stated that no serial killer had ever before turned himself in.
On that point, he was wrong. Both before and after Ford surrendered in 1998, there have been cases of men who have stopped themselves from killing again by going to the police to confess. Some actually express remorse, and might indicate that they'd been on drugs or were in some other state of diminished mental capacity during their crimes. They might also have come to the realization that, try as they might, they cannot stop themselves.
The most famous example of this is William Heirens in 1945. While he did not actually turn himself in, he did leave a message on the mirror of one of his second of three victims, written in lipstick: "For heaven's sake catch me before I kill more. I cannot control myself.' In other words, he appeared to be horrified by what he was doing when he shot and stabbed Frances Brown, leaving her body draped over a bathtub. However, he then went on to strangle and dismember a 6-year-old child, dumping her remains in such a way that it would be difficult to pin the crime on him. Soon a police officer chased Heirens down after a burglary and he did stop; he was put behind bars, where he is today. While he did not surrender voluntarily, he made it clear with his message that he wished to be free of his terrible compulsion to kill.
In a study of 300 serial killers, it was found that 2.3% had turned themselves in, one way or another. That did not account for those who might have made mistakes as a subconscious way to reveal themselves, but only those who initiated police awareness of them. Interpretations differ as to their intent, and even as to their actual guilt, but it's nevertheless an error to say they never do it.