It refers to a landline. The connection was broken because the telephone line was cut or unplugged, perhaps, not because the other person hung up. You are reading Ian Rankin, I see. :)

We say a phone "goes dead" or "dies" when its battery runs out. 1. I had to call him back later because my phone died while we were talking. 2. I will have to call you back in an hour because my phone is about to die. 3. The iPhone's battery dies so quickly!