Hmm... Seems odd that people would be switching family trees, especially if it means families are dying out (aside from unusual situations like a big who deaffiliates or graduates). I know how hurtful it is to have no "family" (I am a founder and my only little deaffiliated
). But even if you have no "family", you do have a "family" - all your sisters. I think that's what texas*princess is trying to say.
As far as calling it big/little, diamond sisters, or whatever goes - no matter what you call it, you're still doing the same thing. The "older" of the pair makes sure the "younger" one feels especially welcome. She gives her gifts, takes her to dinner, makes sure she meets any sisters she might not have already met, may play a role in ritual, and so on. The difference is that some sororities (ADPi is one) place more of an emphasis on calling the relationship something that doesn't imply a hierarchy - once the "younger" of the pair is initiated, she is completely equal with the "older" sister.