Does anyone have a simple example of how this would work? I can't wrap my head around code evolving during runtime for any arbitrary binary change.
It looks like, however, because kernel modules seem to be in elf format (Don't quote me on that, just going from the code), elf format includes a 'relocation table', which is basically a table that says "this function is located here, and this next function is located here, and ..." for every function in the module. Ignoring why that is actually there, they can take advantage of the relocation table and replace a functions location with the location of the replacement function, effectively overwriting the old one. Even if it's still in memory (I can't tell if it gets removed or not) the code will never be called again.
From there, the discussion mostly seems to be around how to 'stop' the kernel enough to be able to replace the function without resulting in a mess because something was trying to use that function at the same time that you replaced it.
I don't think it can do arbitrary changes, it "only" applies specially prepared changes to the running system by replacing function call targets while tasks are sleeping. The biggest limitation to changes probably is that old and new code runs in parallel, so you can only do changes to data structures that won't confuse the old code. "Simplest" use case might be adding guards against exploits to syscalls.
I can't tell how viable it would be for the new code to build an entire parallel structure and to only switch to this after everything is migrated, or how deep into the kernel these changes could go. Could one fix a file system driver while using the file system?