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When I go to apps, I select clear cache. The cache for the app clears to 0. But only for a second. When I close the window and then go back to the cache data, it is no longer at 0 anymore. It does this with every app. Whenever I do this, no apps are running. I've tried restarting the app and my phone. Nothing works. The cache stays clear for as long as I am on the page and then fills back up as soon as I leave the page.
Most apps retain a small amount of cache which increases as you use the app. You don't say what amount of cache it increases to and what app you are referring to.
Keep in mind that having a cache is a good thing. For example holding a website in Chrome's cache saves data and speeds up loading. Deleting it works counter to how Android and other systems are designed. Unless you are having a specific problem, I would just leave it alone.
You mean that no apps are running in the foreground, and that's not true either. If you see your home screen, the launcher is running. And if you use an app to show which apps are running in the background, you may find that the app you're clearing the cache on is running in the background. Force stop the app first.