Why does Google Chrome leave running processes behind even after closing the browser?

There's an option in Chrome's settings to leave it running in the background if any apps or extensions require it. Most likely you're using such an extension and this option is turned on by default. Google Cloud Print will cause this too.

In more recent versions of Chrome, the Advanced Settings page includes an option specifically to keep or turn off background apps when you close Chrome. Google keep tweaking how to find this setting:

In version 67.0.3396.99:

type chrome://settings/system in the address bar.

In version 44.0.2403.157:

Go to TOOLS > EXTENSIONS menu. Uncheck / deselect ALL extensions you have installed (don't delete them, just deactivated all).

Quit Chrome and check if all tasks/processes were ended. If so, it means one or more of the installed extensions are causing this problem.

Now, activate one by one quiting Chrome and checking the processess for all of each of extensions activation. You will find which one is causing the problem.

In my case the problem "DvdVideoSoft Free Youtube Download 1.0.0.0" extension.