My guess is that these are ROMs and the weaving pattern determines its contents. In the second video, there's an excerpt from how the modules were made in the factory, and while the address wire is weaved systematically through all cores by two people, the programming part was done with the help of an automatic guiding arm: https://youtu.be/-BlivdwXRZU?t=57s

>what happens when the magnet becomes deplolarized?

I guess then you try the same thing floppy disk rescueing programs did : keep attempting to read it until you have enough data to make a stastistically significant bet. It should work pretty well since you get an analog value encoding a digital one to start with.

I feel like there's a really good answer to this that doesn't involve taking the thing apart, but I'm no EE.