Is it possible to have the end of your back rib lodge between 2 vertebrae?

Maybe: It is possible to dislocate a rib attachment onto the spine but it requires significant force and a major trauma.

Potentially: The rib is connected to the vertebrae through some strong ligaments. Theoretically you could tear those ligaments and displace the rib from that position, it is just it would take a lot of force and it is a fairly uncommon injury.