The concept of friendship in Stoicism is explored in Margaret R. Graver's Stoicism and Emotion. The ideal sort of friendship discussed in the philosophy does not necessarily reflect any real relationships that actually exist or have existed, as this is an ideal:
"One should keep in mind that this friendship claim, like all Stoic claims about the righteous or wise person, is made at a normative and theoretical level; it is not a description of historically instantiated relationships. If even the individual wise person is as rare as the phoenix, it is hardly to be expected that two such people would ever exist at the same moment in history. But the claim made here does not concern what has happened or might happen but only what ought to happen. Relationship entails plurality; in order to treat the idealized form of human relationship, Stoics must take plurality as a given and proceed from there."
What, then, would relationships among the wise be like if they were to come together, as in theory they might? The above passages sound several important themes: that there is a likeness or similarity among all wise persons; that wise friendship is in essence a `sharing' or commonality (koinōnia) which involves treating the other as oneself; and that there is concord (homonoia), defined as a recognition that goods are held in common. To these points may be added further statements made in the same context by the Stobaean witness. These indicate that wise friendship includes a level of affective engagement.
'The righteous person is companionable, tactful, encouraging, and in companionship is liable to seek after good intent and friendship.... And they also say that cherishing, welcoming, and being friends belong only to the righteous.'
Of significance here are the terms `good intent' (eunoein), `cherishing' (agapān), and `welcoming' (aspazesthai). For eunoia, agapēsis, and aspasmos are all terms known to us in the context of Stoic affective theory, where they are named as species of eupathic response, the type of affective response found in the wise; specifically, they are all species of the eupathic genus boulēsis or `wish.' Their occurrence here suggests that the ideal form of human relationship is conceived not only as a mutual disposition to act in one another's best interests but also as a disposition to respond affectively to one another. We are to imagine the wise interacting with one another in daily life and, in the context of those interactions, experiencing feelings of warmth and affection.
A very early Stoic claim was that all the wise are automatically friends to one another, even sight unseen. In the Stobaean account, however, that view is replaced by one which allows friendship to be more clearly a personal relationship. Proper civic relations between people who are not personally acquainted do not have to be considered friendships, although it is still true that all wise persons, wherever they happen to live, regard one another as fellow citizens and regulate their actions accordingly. Friendships arise when people who are wise also come into contact with one another and acquire knowledge of each other's character as individuals."
Margaret R. Graver. Stoicism and Emotion (pp. 178-180). Kindle Edition.