Err.... The simulation does not exist in the first place.... It's a mental reconstruction of what happens if Coil performed a different action.
It's a
full fidelity mental reconstruction. It perfects reproduces the actions taken by people as well as the physical interactions and basic laws of the world itself. Coil can flip a coin, and the coin lands the same in both realities.
And based on the processing power we have seen shards use, as well as the lack of moral encumbrances on entities, there is no reason to not assume that it creates
full simulations of people, inside that simulation, each time it begins to run a new one. Processing power is not something Shards need to conserve in any way. Dinah's predictive powers are global in scope, and that's not even taking into account the Path.
If that's the case, then although Coil's power is technically a simulation, the people inside it are no less real for being simulations. If you think that they don't exist simply because they aren't physical beings, you also would have to deny personhood to Dragon, Weld (who has a complete metal body, and so whose software must be running on his shard) and Alexandria (who by WOG is running on her shard).
In effect, Coil's power creates an infomorph version of you, running on the hardware of his shard. Because the entities have no sense of human lives as important or meaningful, and as the universe is purely deterministic, when the simulations ends, your eigenself in the simulation also ceases to exist.
From inside however, the simulation is perfect. You have no way of knowing whether you are in the simulation or not. So when you are standing in front of Coil holding the gun, there is an equal likelihood that you are in the simulated timeline, and by firing you doom yourself.
Edit: Though to be fair, if the universe is perfectly deterministic, you never had any choice anyways, and you have no way of exiting the simulation or surviving beyond the point its calculated to end, so you may as well stick it to Coil on the way out.