Finished the MSQ - Feels bad, pushed to do evil [Spoilers inside]

[Loggos]

Depends if the storage is ram or ssd. But even then, if it's long term storage, there is the philosopical question if each iteration of a memory can be deemed as the same person or someone else. So even shutting it down temporarily would condemn every active iteration.

Though judging by the urgency from Schene, it was foolishly stored as ram meaning the memories were lost when the bank got shut down.

Funnily enough, the endless are occasionally "turned off" inside the unlost world and they still consider themselves to be the same person (that doesn't mean they are right, but their perception is interesting).
They can get destroyed and have to be recreated. The guy with the ring tells us he has already been "reincarnated" (recreated by the system) 3 times but can't risk getting destroyed by the monster, that stole his ring, another time because recently there is so little energy that fewer and fewer endless get restored. That sounds to me as if they are stored long-term. So if we were to turn the power on again they would probably perceive themselves as the same person even though you could argue they are not.