Keilim, Chapter 11, Mishnah 9. This chapter is occupied with metal utensils and the conditions under which they are susceptible to tumah. Our mishnah applies those rules to a piece of jewelry: an earring, and specifically an earring that has broken into its separate pieces.
Before the mishnah can be read, we need a picture of the ornament it is describing. The earrings of that era were assembled out of two separate components. The lower component was shaped like a miniature cooking pot, with a hollow interior. Fixed on top of it sat an ornamental piece whose form resembled a lentil. Extending upward from that piece was a hook, which was threaded through the pierced lobe of the ear and held the whole ornament in place.
The earring that comes apart
The mishnah's opening case is an earring built exactly that way: "nezem", an earring, "she'hu asui kikedera milemata", whose bottom section has the form of a pot, "veha'adasha milema'alan", with the lentil-shaped piece sitting on top of it. Then something happens to it: "venifrak", the ornament fell apart, and the two sections are no longer connected. With each section now standing on its own, the mishnah issues a separate ruling for each one.
The pot-shaped base
"Kakedera tameh mishum keli beit kibul": the piece shaped like a pot is susceptible to tumah as a utensil that has a receptacle. Its hollow was not merely decorative. Women would place a fragrant substance inside it, so the little pot genuinely served as a container. Since it is metal and since it holds something, it qualifies as a keli with a beit kibul, and a metal utensil with a receptacle can receive tumah.
The lentil-shaped upper piece
"Veha'adasha tameh bifnei atzmo": the lentil-shaped part is susceptible to tumah in its own right. Even though it no longer has the little pot beneath it, it has not lost its identity as a utensil. The hook is still attached to it, so it can still be fastened to the ear and worn as an earring exactly as it is. A piece of metal jewelry that continues to function as jewelry remains a keli, and therefore it too can become tameh.
The hook alone
"Tsinorah tehorah": if the hook itself becomes detached, it remains tahor and can never receive tumah. The reason is that the hook has no independent use at all. It is never worn or used by itself; it exists only to hold the earring in the ear. Once it stands alone it is not a utensil, only a part, and a mere part is not susceptible to tumah.
The cluster-shaped earring
The mishnah closes with a second type: "he'asui kemin eshkol venifrak, tahor". This is an earring fashioned to resemble a cluster of grapes, made up of four or five beads gathered together. If such an earring came apart, all the pieces are tahor. Here no single bead has any use of its own; it is only the assembled cluster that forms the ornament. Once the cluster has been undone, what remains are individual beads that are not utensils, and so they cannot receive tumah.
The principle that runs through the entire mishnah is a single one: after a metal object breaks, we ask about each surviving piece whether it still does something. If it holds, like the little pot, or if it can still be worn, like the lentil with its hook, it is a keli and it is susceptible to tumah. If it is only a fragment that serves nothing on its own, like the bare hook or a lone bead from the cluster, it is tahor.