This is not a big bad danger but if you have a piece of brush lets say that is too close to the fence a spark may and in some cases will jump from the wire to the dry brush so it can go to ground.
Remember that dry objects are much less attractive to electricity than wet objects are. If this was not so then the prison guard would not put a sponge soaked in salt water under the skull cap thing on the electric chair.
The greatest danger of fire is when someone gets lazy about keeping weeds and brush from growing up under or in among the wires on the fence.
Remember that an electric fence is a dumb machine. You have to think for it because it only follows the laws of nature.
The fire potential is almost nonexistent in most of the country but in the Prairie States or in drought stricken California the danger is greater because of less moisture in the vegetation.
Electric fences are metallic by nature and metal attracts lightning. The danger is mostly to your charging unit because I know I am, and I doubt that you are machesiom enough to grab a working electric and hold on to the sucker for hours during a lighting storm. Most people dispense with the arrester because the shorter the run of fence wire the less likely that your fence will get zapped by a bolt of lightning.
Despite the old wives' tail about lighting only striking once, lighting tends to revisit the same sight over and over.
When there is an
open short the fence will arc across that space, this spark or arc is the fire hazard, just like it arcs to a spark plug or to the fox's nose in this video. Note that the electricity didn't lay the fox out ready for the undertaker but that the fox though that the undertaker already had him in his grasp, he keeps his distance and keeps looking back over his shoulder at the chicken coop that "bites" back. This is how electric fences work by training the vermin to stay at arms length from you chickens.
I like the following video because it shows how effective motion activated flashing lights are at deterring foxes and other predators from snacking on your poultry.
Note: Watch the front left corner of the hen coop about, 12 - 15 inches above the ground and watch the night light go crazy. Also foxes can clear a 7 foot fence if it really must have to do it.
Finally here is what happens when the fox eventually breaches your defences.