No need to start two threads on the subject.
Looks like an ordinary bi-pin socket. Buying just one or two will not be low cost. Shop eBay or Lowes. If going to Lowes, take the old one with you even if it is broken.
I have repaired those sockets with Super Glue. Figure out how it will be clamped before applying the glue. Rubber bands?
I have had numerous technical problems at eBay recently.

Separating the pic from the description might make this difficult for people to answer.

A clearer pic would help. Despite that handicap I am willing to guess that that black ring is supposed to rotate with the pins and has slots in it for the pins. They sometimes get out of alignment and have to be rotated back where they are supposed to be before a lamp can be inserted and rotated into the correct position.