Used to work for a company as a CS agent working from home, on my own PC, telephone and internet all paid for by myself, and I was a paid employee, not a self employed 'worker'. As part of the process of working, you have to install dialer software that runs on the PC to enable telephone calls to be answered via a constantly open telephone line, managed by said software. The actual work interface was via *cough spit* Citrix.
A few months in, I'd noticed some odd CPU activity, and noticed there was a VNC viewer installed, without my knowledge. It turned out that the dialer software quietly installed WinVNC, and ran in the background. Further digging revealed that the software not only had the option to show my desktop (not the Citrix side - Mine) which apparently was never actually used, but was also a keylogger which WAS used.
I asked my line manager exactly why did they need to know what I was typing outside of the Citrix environment, given it was my own machine and internet connection. The answer? To make sure I wasn't doing anything in work time unrelated to the job.
Happily, I discovered that I could easily block both VNC and the keylogger, and noone seemed to notice. That of course wasn't the point, as I certainly don't remember giving permission for my personal computer to be bugged in such a way.