If the app attempts to access system files or other running processes then it has to make a call to a system process to do that. The system process simply refuses the request of the sandboxed app. Apple doesn't have to allow any sideloaded apps to run outside of the sandbox.Only when installed from the Apple App Store, apps installed from Cydia and other jailbroken app stores do not have to run in a sandbox. So unless Apple Approves all side loaded app stores (not sure how that would be possible) then there will be apps that can be installed without being sandboxed.
An exploit can be used to break out of the sandbox. It tricks a system process into providing access or executing code where it shouldn't. Jailbreaks rely on exploits to work and modify the system to no longer run apps in the sandbox. As we've seen there are jailbreaks that work even without first running a sideloaded app, although sideloading would theoretically make it easier to use some types of exploits. Breaking out of the sandbox is a very difficult task which many brilliant people have failed at, and there's a nice reward waiting in Apple's bug bounty program for any white hats that are able to, so have at it. When they are discovered, they are quickly patched by Apple.
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