KeBugCheckEx(), the method that displays a blue screen, dumps memory to the paging file (which is contiguous and fixed, so it doesn't need the FS driver). When a dump is about to be made, it hashes all of the pieces of the pager and the disk driver necessary to do the dump, and ensures that they aren't corrupted, then dumps. On reboot, the boot manager notices that the system died messily, and copies the paging file to a crash dump.

Now you know more than you ever wanted to about blue screens. :)