Narcissists cannot be alone. Narcissists need people more than anyone. They have very specific reasons for being in relationships, but they are not built on the universal need we all have, which is to love.
Narcissists do not enter or stay in relationships for love. Their motives are quite different. They become involved in relationships in order to ensure their needs are met and someone is always present to provide them with the attention and adoration they require in order to feel alive.