When a narcissist refuses to give you closure, there are a couple of things going on.
First of all, they want to elevate their own sense of low self esteem to one of grandiose superiority, therefore they stop talking to you in order to make their own self appear to be worthier or better than you or anyone they choose to use as a stepping stone to manufacturing a false high – “I’m superior. I don’t have to talk to you.”
Secondly, they want to punish you for any reason they’ve set in their minds. You may have criticized them, therefore you become an instant enemy and must be taken down a notch. They hate anything that points out they could be other than perfect. If you even bother offering any kind of constructive criticism, they’ll retreat, taking it as an attack. When this happens they go ballistic, and like any irrational person they become extremely violent in their treatment of you. Both in their words, but especially their actions.
Now, someone who lashes out, or stops talking to you in order to get revenge for really nothing that you did wrong definitely does not wish to give you closure.
By refusing to give you closure, they are putting themselves in a position to have the upper hand. They will punish you and make you feel bad. They’ll feel superior to you; more powerful by hurting you in this way. In theory, if they were to give you any closure, that would only work against the Narcissist as it would allow you to heal and move on from them. Instead, they would rather make you continue to feel discarded in order to prove, simply by being uncaring and vindictive that they are more powerful than you are. But that is simply not true.
Once you see the truth of it you will realize that there is nothing you can do to help them to improve, communicate their true feelings to you or move towards a better relationship and dialogue with respect. They can’t even be honest with themselves. They’d rather deny any sense of inadequacy and go with the belief they are superior. Since they spend a lot of energy and time perpetuating a lie, they will never enter an honest and constructive dialogue with another.
At the end of the day, don’t feel bad about not getting closure. The minute you realize you shouldn’t or don’t need it, you will have the closure you seek.