Based on the Prefect documentation, the Prefect Scheduler service is responsible for creating new flow runs and placing them in Scheduled states; it does not affect execution. If you change a schedule, previously scheduled flow runs that have not started are removed, and new scheduled flow runs are created to match the new schedule.
In regards to scheduled flow runs being deleted when stopping the scheduler service, it is not completely clear from the documentation why this would happen. If you have a specific behavior that is unexpected or a reproducible issue, I would suggest searching GitHub issues for similar reports to see if it's a known problem or if a solution is suggested.
For more information, please refer to the scheduling section in the Prefect documentation
here. If you're facing issues with cancellation of flow runs, you might want to check out
this section on flow run behavior during cancellation.