Shoutbox

It is physically impossible for the webcam, connected via the computer to the network, to keep on functioning when the PC is turned off.

When the PC is turned off there is no power to its internal hardware and thus there is no software running. There needs to be power in order for a PC to function.
A normal webcam needs to have at least a driver running on a running operating system, this also includes RAM. When the PC is off there is no OS running, there is no RAM, there is no driver. None of these means no picture...

Note that turning a PC off might take a while (especially if updates are being installed), in which during that time a webcam picture may continue to broadcast for a very short while.

So if it happened it very obviously means the PC was _NOT_ (yet) off at that time.

Again, it is physically (as in 'laws of nature') impossible for a webcam to function when the PC is turned off.