I recently had a "fence situation" at one of my rentals. One side of the backyard fence was rotted and parts of it were falling down. The neighbor on that side (also renters) has 2 large dogs that could (and did) easily get through the fence, which concerned my tenants. When I bought the house a couple years ago, the survey clearly showed that section of fence on the neighbor's property and the "good" side was facing them, so I assumed it was their fence.
I contacted the owner of the neighboring house and explained the situation (fence condition, dogs, survey). He had no disagreement with the situation. I offered to pay for half the new fence and handle the logistics. He was cordial and business-like, but refused to have any financial involvement. He claimed that the fence was already there when he purchased the lot and built the neighboring house 25 years prior. Our house is much older and he insisted that the fence is our responsibility despite it being on his property. He also explained that his tenants had never complained about the condition of the fence, although he was surprised it was still standing.
At this point, I considered playing hardball, but it was becoming clear his position was unlikely to change. In this part of Texas, fence cost sharing is a gray area and highly subject to the personalities involved. Had he called me with the same proposal, I would have agreed. I ultimately decided to pay the whole cost myself and just get it done. My tenants already had strained relations with the neighboring tenants over the dogs. So I decided to not make the situation worse by taking on the owner, who said he would speak to his tenants about keeping their dogs contained until we fixed "our" fence. The old fence came down, new fence went up, and both tenants are happy and getting along a lot better.