I haven't used Windows in many years, but back in the day adware would get itself bundled with native applications' installers - for example, you download and install Java on Windows, they try to trick you into installing a toolbar.
Once your adware is installed as a native application, you simply install two copies, each of which immediately reinstalls and restarts the other should it get removed/stopped.
This is a Chrome extension - they're supposed to be sandboxed, and unable to pull such tricks. If it really couldn't be uninstalled from the installed extensions list in Chrome, I'd love to know how they did it.
Once your adware is installed as a native application, you simply install two copies, each of which immediately reinstalls and restarts the other should it get removed/stopped.