"Once had a fax try repeatedly to connect to my parent's house number. Drove us all mad (I was living at home at the time)."
I had this happen too. The much simpler solution was to grab a fax and plug it into the line - to discover that my home number was the same (but a different area code) as a major finance company's fax line.
After the company ignored complaints about their agents faxing the wrong area code, we took to faxing back the (highly senstiive) application forms with "APPLICATION REJECTED. POOR CREDIT RISK" in scrawled over the top of the form in large black marker
The calls stopped after about a week
Another person I know took a similar path and found out the home number of the CEO of a company whose fax machine was dialling out at 2-3am then rangi that CEO up every time he received a 3am fax call - at 3am.
Unsurprisingly the 3am fax calls stopped happening within days.