It appears there are no open issues in the PrefectHQ/prefect repository that exactly match your situation with ECS Fargate tasks continuing to run after a flow stops. This could either mean that it's a unique issue that hasn't been reported yet, or it may not be a common problem.
The behavior you're describing is not expected—the ECS task should normally be stopped when the flow run is stopped. Here's what you could do to try and resolve this issue:
1. Check the configuration of your Fargate task to ensure it's set up to handle shutdown signals properly. This often involves configuring the application within your Docker container to respond to shutdown signals from ECS.
2. Look into your Prefect flow's code and the way you are deploying to Fargate. Ensure that the shutdown and cleanup procedures are correctly configured.
3. Verify your Prefect version supports the desired behavior with ECS Fargate. If necessary, consider updating to the latest version of Prefect.
4. If you aren't able to resolve the issue, consider raising an issue in the PrefectHQ/prefect GitHub repository with details of your setup and the behavior you are experiencing.
5. As a last resort, you can implement a custom solution to monitor your Prefect flow runs and programmatically stop ECS tasks whenever a flow is manually stopped. This would likely involve using the AWS SDK to interact with ECS directly.
If you're able to provide more details or specific logs/errors you're encountering, that might help in giving a more targeted solution.