I misunderstood. Ignore the previous post #15.
Twisted pair has a capacitance of ~20pF/ft
1200 ft of line would have a capacitance of ~20*1200 = 24000pF = 24nF
If the line is intact, that is shunted at the far end by 282Ω in series with whatever the solenoid inductance is.
If the line is open, it will have a bit of residual capacitance but the solenoid inductance and resistance would not be there.
Your idea of injecting some DC bias through a 50K to 100K resistor will work (use high voltage resistors for R1 and R2, check breakdown voltage).
Here is my proposal:
There are three periods shown, each lasts 50ms in the sim.
1. normal 120Vac applied to distal relay.
2. normal line, 120Vac is off.
3. Faulted line, 120Vac is off.
Note V(out) at each period. V(out) is sampled by the AD in your microprocessor. You will have to discriminate as to what is happening on the line in your processor.