In Alpha Gamma Delta, if I'm not mistaken (and sisters please correct me if I'm wrong) the Badge remains the property of IHQ and upon Initiation, each member purchases a lease on the Badge.

If a member becomes suspended, she must return the Badge.

If a sister enters Chapter Grand, she has the option of being buried with her Badge or disclosing on the Badge disposition form that her family is to return the Badge to IHQ. I think it's important for all sisters (whether it be within my own organization or NPC) to inform their next of kin on what to do with the Badge after their passing. It's the only way we'll keep them out of non-member hands.

Personally I don't know of any sister who collects Badges. I know of many who rescue them off of greedy sellers on eBay, but those sisters ultimately send them back to IHQ.