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A narcissist engages in hierarchical thinking, meaning they are always judging people by one or the other of several ranking systems (that not everyone judges by since at least some of us recognize that we are all different but equal). These systems could be wealth, looks, fame, success, power, intelligence, fitness, status, etc. So a narcissist sees his or her various sources of narcissistic supply (the people who give them attention, approval, admiration, acquiescence, or agreement) as one being above or below the others. If someone is given higher rank than the others (in their own mind) a narcissist will keep trying to get back into their life to see if they can elicit some emotional response from them, positive or negative. Some may want to see if they can seduce you again, while others may want to see if they can make you angry and still others may want to get revenge (especially if you left them rather than vice-versa). Those who want revenge may just want to scare you or they may take it as far as actually assaulting you or your property.
If their goal is to seduce you and you have actually seen through their pretense of love to the point where you have zero feelings for them anymore, they are likely to move on to try and find someone they can seduce. If, however, they are malignant narcissists and their goal is to terrorize you by either making you feel threatened or by some kind of actual assault then short of having them incarcerated (which could only be for a short while creating even more desire for revenge when they get out) then you may have little control over the situation as long as they know where to find you. (I had to relocate to avoid one extremely violent malignant narcissist who stalked me from Georgia to Arizona after seeing my address on a letter he found in my mother’s house)
For a malignant narcissist the act of overpowering and terrorizing their victim is a source of negative narcissistic supply that a narcissist sadistically enjoys. A malignant narcissist enjoys the feeling of power that is derived from tormenting and torturing a victim. They feel that this is justified in their world view as their rightful position to punish anyone who does not give them what they want and/or feels entitled to. Irrational and incomprehensible as this may seem to a normal person, dominating a victim is how they try to seek relief from their own feelings of having been diminished in some way.
This is often but not always from past abuse that could be: emotional (like neglect and being unloved), verbal (overly critical parenting or as a spoiled child being expected to live up to unrealistic ideals rather than just letting them be a kid who gets muddy, spills stuff, etc…), physical (that makes a child decide THEY want to be the bully in control) or sexual (which may make them want to be the dominant one in relationships because they got dominated and exploited). Their feelings of inadequacy could, however, also arise from simply being rejected or slighted by someone in their past.
The relief derived from the act of ‘punishing’ someone, who may be a stand in for their real or imagined offender, is only temporary because they still have the same thoughts and feelings that drove them to act out their revenge fantasies to begin with. Without self awareness or therapy they will still be tormented by their inner critics/inner demons and continue acting out their sadistic desires even if their victim had nothing to do with the incident that made them feel so inadequate that they wanted to somehow get revenge on someone (as a stand in for the original offender).
If they are non-malignant narcissists and are seeking merely the narcissistic supply of being able to re-seduce you then they will quickly lose interest if you really no longer have any feelings for them but they can sense if you really still want them from your body language and the way you look at them so to really get free of them you have to resolve your own feelings and learn to see through the act of lovebombing. Recognizing that they try to seduce so as to once again have an opportunity to prove their superiority by flipping and devaluing you (a minor form of sadism) is key. If they have shown a pattern of devaluation in the past they will continue with their habit of lovebombing/devaluing so long as you fall for their efforts at seduction.