"Super glue is generally not flammable when dry, but the liquid form can be a fire risk due to its chemical composition. It's important to keep it away from flames and heat sources while in its wet state." I don't plan to use the lighter socket for smoking while the glue is wet, or ever!
There apparently are special tools to remove and replace the socket. Maybe removal was attempted without such tools, which is why it's loose. Anyway, I superglued it in place and it's now rock solid. My MP3 Transmitter in the socket is close to my elbow and it doesn't get accidentally knocked around to where I can't see it.