Neighbor Appears To Be Deliberately Letting Their Fence Fail To Pressure Us Into Paying Half. Concerned About Negligence Liability. [utah]

Location: Salt Lake County, Utah

Our jurisdiction has no automatic 50/50 cost-sharing requirement for residential fences.

Our neighbor's wooden fence runs along the side yards between our properties, tucked behind both of our garages. It's not visible from the street, and we have no practical use for it — we don't even close our own gates. The fence began leaning badly enough to threaten damage to one of our trees, so we contacted the neighbor and asked them to fix it.

Rather than addressing the repair, they asked if we'd share the cost of a full replacement. We declined, for three reasons: the fence is repairable, it serves no function for us, and we've successfully done this exact repair with a prior neighbor.

They responded by claiming our bushes, vines, and trees had caused the damage and that repair was impossible — seemingly believing this accusation would obligate us to pay half of a new fence. They sent us photos showing a brace they had installed to support the leaning section.

Those same photos, however, showed something more significant on their side: the worst-leaning portion of the fence has a foot-high raised planter built directly against it. A downspout from their garage drains into that raised bed roughly one foot from the fence. Additionally, their garage roof pitch directs snow runoff directly to the base of the fence, which sits in shade and stays damp.

Regardless, we immediately trimmed all vegetation on our side to eliminate any basis for their claim. The real issue is straightforward: this is approximately a 30-year-old fence with wooden posts set directly in the ground. Every post is rotted at the base. There was no visible evidence of plant damage. I have photos documenting rotted posts on a sample of them — I didn't excavate every post, as I didn't want to cause additional damage to the fence in the process.

All of our communication with the neighbor has been by text message. We informed them that the posts were rotted and that the fence is repairable, and received no response for several weeks.

We recently discovered they removed the brace visible in their own photos, the one that had been holding the fence up on their driveway side. They are now parking a newer car directly next to the unsupported, leaning fence.

UPDATE: We have thought, since we moved in 20+ years ago, that the fence was built by the prior neighbors and is their property. One of the posts is 8 feet tall vs. 6 feet everywhere else. This taller clearly-original post helps form an arch that's attached to their garage. There's a gate there. This creates a hidden area for their garbage cans beside the garage. This is a 1950s subdivision, so nothing is built to modern offsets.

My questions:

1. Does deliberately removing structural support from a failing fence — after being put on notice in writing that the posts are rotted — constitute negligence or something stronger if it falls and damages property?
2. If the fence does fall and damages their car, are we exposed to any liability given our vegetation was trimmed and the documented causes of failure are on their side (rotted posts, raised planter, drainage, shade)?
3. Is there anything proactive we should be doing right now to protect ourselves?