Suppose that I have a program running on a modern CPU. Let us suppose that I also have a way of running programs through some much more advanced mechanism: say, some hypothetical sophisticated computer that runs on photons. Suppose my technology is so advanced that I do not even need solids to confine the photons, but I can use gas or plasma or EM fields or whatever. Now, I can couple those two systems, so that the programs are running on the CPU, but if they need to use the resources of my super-advanced light computer, they can reach out and execute instructions on that computer instead.
Now suppose that I go one step further. I have the system set up so that if the conventional computer degrades too much to continue running its programs, those programs will be transferred in a rapid and completely continuous1 fashion to the trapped light computer. Thus we do not need to be overly concerned about whether it is still the same operating system, since there is no sharp transition point between when it stops running on the conventional machine and starts running on the light computer. Since I am building the system, I get to determine its behavior, and I say that merely damaging it without rendering it incapable of running will not trigger the transfer.
Why not just use the optical computer? I am the system designer, and I like conventional computers, so I can do whatever I want. The optical computer is there because I want my system to be robust if the conventional computer fails. Maybe the conventional computer was created by a completely different process, or even by extraordinary random chance and the accumulation of useful innovations, and I am just adding something on. Also, maybe it is slower, like real-life optical computers in 2020, so that the programs are limited in their ability to evolve once they have fully transferred over. This might also mean that to a program on the optical computer, centuries could seem like the blink of an eye.
Does damaging the CPU also damage the optical computer? Not usually, since the systems are fairly isolated except in exceptional circumstances. Still, maybe there is some powerful electric surge or something similar that would overwhelm those protections and damage the optical computer as well.
Please feel free to replace the conventional computer with a human brain, the optical computer with a soul, and make any other appropriate substitutions.
1: At least from a macroscopic perspective.