Good explanations, [MENTION=1206]cascadeco[/MENTION] -- thanks! Very thoughtful and much more cohesive than I would have done.
Friendships. Any friendship that is a part of a "group of friends" that you're also a part of. Also it's good that you're asking these clarification questions, because I just realized that one pretty common definition -- i.e. an obligation to obey social rules for the sake of harmony -- is NOT what I was talking about before. As I was referring to it, your social obligations, as they relate to a "clique" of friends, are your obligations to individual members of the group, collectively. When I say "people will miss you when you're gone", I'm thinking of individual people who will miss you for their own personal reasons, because they all individually like you.
My explanation above is VERY so/sx -- but that's probably because my annoyance with social-last "disappearing" is very linked to my instinctual variants. Since figuring out that I'm so/sx, I've realized that my social scene is very true to type: I tend to collect people I like individually, and form them into a group around me*. So when one individual decides to not participate in things socially, or decides to leave without warning, or some other clueless social thing like that, because "no one will miss (them)" -- they clearly aren't realizing that the group is made up of individual people who care. At best, the reaction is like Qlip's reaction below: aw, they're clueless, that's cute. At worst, it's cause for resentment; we the group members are putting effort into this, by creating occasion to hang out, and you clearly aren't putting in any reciprocal effort.
Not sure if this is related or not, but I've also had social-lasts bail on completely non-group-oriented, just-the-two-of-us things because they simply weren't in the mood, and they assumed, since I'm the socially savvy person I am, that I'd have back-up social plans and wouldn't mind.

Completely baffling, and, when it's happened, hard not to take personally.
*Just realized my blog is a pretty great example of this.