Its completely possible to run on only 1 wire. I have seen it happen a few times before - Obviously with reduced performance. ADSL is not carried by the DC on the line, its more like a radio signal. Because of this, it treats a break in the wire more like a capacitance then a disconnect. If the two ends of the break are close to each other, then its quite possible that you will get signal passing but if they are too far apart then it will be attenuated too much to be usable. The more likely answer is you had a break on one of the connections in the exchange - the part of the exchange dealing with telephone comes first. This is connected to the DSLAM for data, and that is connected to the user. If there is a break between the Telephone section of the exchange and the DSLAM, it will mean that you have DATA but no landline service.