I believe I had to sign something, with Gamma Phi Beta, that said that I understood that my badge was property of the sorority and not my own, and that in fact I was leasing it for life.
But with Gamma Sig, our badges are inexpensive, and they are easy to buy direct from the jeweler. When I bought my replacement badge, for the one I had lost, I did it from the jeweler, and there was no proving my membership, which I thought was kind of odd.
I know with Gamma Phi, and most socials (at least NPC socials) we buy our badges direct from our international office.
It's sad to see badges for sale like this, and hopefully maybe our national office can come up with a program to save them from ebay, like Crescent Catchers, or Kappa's Keepers of the Key (I think it has another name now... not sure).