detect if open wire has been cut after test point
One way that could be possible to detect in open-circuit situation, by measuring the capacitance between the two wires, supposing they are within the same cable for most of the way.

To do so, you can inject a high frequency signal and measure the phase shift between the two wires. 

If the capacitance changes (is reduced), it is likely the length was changed.

Also the final device input also probably have some capacitive signature that would improve the detection.

If the signal is closed, simply inject a small current as you said.

Here some example.