Stuck valve stem core

This is actually not on my KZ tube... it's the valve stem on a TPMS valve on my car. When I go to remove the valve stem core, it turns counter-clockwise until the small bar which the valve core tool grabs is almost flush with the top of the stem. Then it just spins. I can turn the core back in all the way using the valve core removal tool, and it seats fine (when it stops turning, that feels "normal"). I can air-up the tire and let air out as normal. Just can't remove the core.

Wondering if I should try working some silicone spray down into the core. I plan to pull the tire off the wheel, but it's going to be a pain, with the core stuck in there.

It spins because it's got to the ends of the threads.
It should just pull out.
You may need some tweezers or needle nose pliers to get hold of it .