To us, it seems that human relationships require emotional investment in another person. If you have a friend, or someone whom you love, you grow to feel you "need" them, and feel an acute sense of loss when you "lose" them in some way. The ancient Stoics, as Margaret R. Graver shows in Stoicism and Emotion, had a very different take on the issue:
"Perhaps the most radical element in the Stoic theory of friendship is the claim that relations among good people can be warm and genuine without also compromising the self-sufficiency of the individual. An important feature of the normative human in all ancient accounts is that he or she has the resources to live happily in any and all circumstances. Real happiness should be such as cannot be destroyed by any possible kind of loss. It follows that the wise person should be unalarmed by the mortal illness of a friend and should not grieve when friends die. While there might be some tears and a certain amount of pain-for these can come on involuntarily, as a `biting and small contraction'-there is no possibility that the wise will enter fully into grief.
The claim that friendship is compatible with self-sufficiency could be defended in two ways. One could argue, first, that the ability to rise above the loss of friends comes of the wise person's accurate understanding of what it is for a thing to be good. The value of the commonality between friends is in its harmonious nature, and this is not dependent on numbers or diminished by the removal of one person. Alternatively, one might argue that while the wise value friendship in general, they are unconcerned about the identity of any one particular friend. A wise friend of one who is gone will turn immediately to other friends or potential friends, finding in them the same source of satisfaction as existed before."
Margaret R. Graver. Stoicism and Emotion (pp. 182-183). Kindle Edition.