Hitting stop kills the app instantly. No dealloc or other code gets called (notably none of your application delegate methods that may be saving data), the process is just terminated. All of the memory used by the process is then freed, and when you start again, you're starting from scratch.
This is unlikely to be the cause of "random memory" problems. If you can give more detail about the symptoms you're experiencing, there could be more to say.
The best way to simulate what a user might do is to hit the home button, then stop the process. This doesn't terminate your app, but you should be dealing with everything necessary when entering the background anyway.