TL;DR: Shut down of the simulation may be observed and may be unpleasant and it is especially likely if there are infinitely many simulations. It will look like very strange global catastrophe from the observer point of view.
There is a possibility of something like quantum immortality for many simulation world. Thats is if we have many identical simulations and some of them will shut down, nobody will feel it and it will not have any observable consequences.
Lets name it "simulation immortality" as there is nothing quantum about it. I think that it may be true. But it requires two conditions: many simulations and identity problem solution (is a copy of me in remote part of the universe is me.) I wrote about it here:http://lesswrong.com/lw/n7u/the_map_of_quantum_big_world_immortality/
Simulation immortality precisely neutralise risks of the simulation been shut down. But if we agree with quantum immortality logic, it works even broader, preventing any other x-risk, because in any case one person (observer in his timeline) will survive.
In case of simulation shutdown it works nicely if it will be shutdown instantaneous and uniformly. But if servers will be shut one by one, we will see how stars will disappear, and for some period of time we will find ourselves in strange and unpleasant world. Shut down may take only a millisecond in base universe, but it could take long time in simulated, may be days.
Slow shutdown is especially unpleasant scenario for two reasons connected with "simulation immortality".
- Because of simulation immortality, its chances are rising dramatically: If for example 1000 simulations is shutting down and one of them is shutting slowly, I (my copy) will find my self only in the one that is in slow shut down.
- If I find my self in a slow shutdown, there is infinitely many the same simulations, which are also experience slow shutdown. In means that my slow shutdown will never end from my observer point of view. Most probably after all this adventure I will find my self in the simulation which shutdown was stopped or reversed, or stuck somewhere in the middle.
See simulation map here: http://lesswrong.com/lw/mv0/simulations_map_what_is_the_most_probable_type_of/