The person who arrived alone deserves to be included before they prove they are entertaining.

Groups tend to hand out belonging as a prize for being good company. Whoever arrives alone has to perform their way in: be funny, be interesting, find the opening in a conversation already moving. The people who most need a welcome are least able to do that in a room of strangers, so the ones who leave early are rarely the ones who were unwilling.

At the next gathering, find the person at the edge in the first ten minutes rather than the last. Introduce them by name with one detail attached, so someone else has a way in. Then stay a minute, since leaving immediately undoes most of it.