Encountered a mysterious issue these days: stopped the App Service on Azure, but the application was still logging, like nothing happened. Waiting couple of minutes, then half an hour, but logs were still coming.

Checked the generated url and the site responded as it should:

Turned out, that the App Service was hosting WebJobs, not a classic web app and the default “Stop” doesn’t apply to them. To turn off WebJobs, one need to navigate to WebJobs blade of the App Service.