Avast: Free, up-to-date everything.
Active shields: Web, File System, Behaviour & Script
Shortly after having used a VPN and then disconnected, I noticed residual net traffic & CPU usage.
Wireshark revealed that AvastSvc was polling (successfully) http://files.avast.com/files/vpn_ssid_notif.txt once a second.
A reboot was required to stop it.