This is a scenario I have come across many times in my career and it always confuses people! The telephone line feeding your property is known as a pair (2 separate wires). This carries a 50 volt signal which is needed to make phone calls. Sometimes a fault occurs on just one of these wires meaning that the telephone line goes dead, but the broadband still works. This is because it is only a data signal, which does not need voltage on the line to operate, just a metallic path back to the exchange so will sometimes work over the one good wire. Generally however, the speed of the broadband will be lower and less reliable.