I don't think so - they'd just be responsible for fixing that if it fell down...
It should be confirmed somewhere in the deeds/land registry though, so if it isn't you might have a case for sharing the cost? Probably a lot of hassle and cost, just to get one over on her for being a sour bitch...
I'd say it's your fence (#179 right?), otherwise, #180 is responsible for the fence/boundary on both sides of their property and someone on the run has no responsibility for a fence/boundary.