Question: In the Flashpoint episode "The Farm," there's a scene where you can see one of the officers run a jumper cable from one contact on an electric fence to another, then cut the line of the fence (not breaking the circuit, mind you). Based on context clues, one could assume the fence surrounds a large, multi-acre plot of land. Another bit of information: the cable they used to keep the circuit complete was longer than the original cable on the circuit, which would mean it would have a higher resistance when the circuit was rebuilt.

I have two questions:

1. How feasible is this?
2. And would a (powerful, that is) fence controller be able to detect the change in resistance? Or would it be so small that it's undetectable in the grand scheme of things?

From my (limited) electronics/electrical schooling, adding the cable to jump between the contacts would change the resistance, as resistance for parallel circuits is modeled as:

$$r\_{total} = \frac 1 {\frac 1 {r\_{a}} + \frac 1 {r\_{b}}}$$

Which means the addition of the extra cable would have an impact on the resistance of the circuit itself (although very minimally).

If I recall correctly, another one of the officers was counting down to when the first officer should splice into the circuit. I don't know enough about electric fences to come to any conclusion, but are electric fences constantly charged? Or do they have a delay between pulses?

Answer: 
Even if we ignore all the mentioned variables and assume an ideal fence, the change in resistance would be very small. Assuming the wire's total length of 4,000 ft, at a height of 6 ft. To bypass it, one would need to add only about 10 ft (5 ft down, 5 ft up). With a resistance of 1 ohm per 10 ft, the initial total resistance would be 400 ohms. Adding 10 feet would only add 1 ohm (resistance in series, not parallel), making a total of 401 ohms. This is a change of only 0.25%. Also, there is an additional complication. You can not take measurements of the line while the high voltage pulse is active. This means that to get its resistance (impedance), you have to **sample** the line **in between** the high voltage pulses.
Some car engine controls look at wave forms in ignition secondary wires to learn if & how fuel-air mixture is burning. Some can spark again if burn is not as desired. A fence monitor could measure wave forms of voltage applied & current to detect fence changes. Measuring between pulses is not the only option.
Sorry I do not remember makes & models.