digital subscriber line
About
A digital subscriber line, more commonly known as DSL, is a form of internet service that runs over POTS twisted-pair lines, sometimes on the same pair as standard telephone service.
Notes
Apparently the difference between a live DSL line and a disconnected circuit cannot reliably be discerned with a common multimeter. Short of professional network diagnostic devices costing thousands of dollars, the best available tool seems to be an inexpensive DSL modem (although there may be inexpensive devices available from niche manufacturers; I saw reference to some which might have been available, but no prices or retail sources were given).
It seems unlikely that accidentally reversing the polarity of DSL wires when connecting them to a DSL modem would damage the modem, but likely that the modem would not be able to read the DSL signal.
ISP equipment on the other end is apparently sensitive to momentary shorts, and may trip the equivalent of a circuit-breaker when this happens. The time until reset is apparently variable, and possibly indefinite in some cases (human reset required). Connecting a standard telephone directly to a DSL circuit (without an intermediary filter) might also trip the breaker.