Is it ever possible to gain closure from a narcissist when they end a relationship abruptly with no explanation for the breakup?

A narcissist will say goodbye to you only when he/she has found a better supply of validation in someone else. If they feel that they can still gain ego-points from having you around, they will probably not vanish. They will usually never give closure to a relationship-- sometimes even picking fights with you out of nowhere and after months of not speaking in order to assess whether or not you still care about them.

The important thing is not their actions and reasons for why they do what they do and how they do it, it's your health. You have to seek help (best with the guidance of a professional therapist) and find the root of your need to have a narcissist in your life. Though they can be charming, good-looking and magnetically talented individuals, the reasons for why we stay hooked on them are not usually about these pro attributes but are about the familiarity of the relationship dynamic from our childhood.