Unless negligence is involve (like an arborist being hired to condemn a tree), they’re generally considered and act of god. They’re the responsibility of the property they fall onto.
So, in the case of OP, the situation is unfortunate, but it’s on him to maintain his properties and his fence lines within his properties. It’s convenient the state has a fence along part of his property, but it’s not their responsibility to fix it for adjacent lots.
Practically you’re right of course, but they are probably technically responsible given the circumstances the poster laid out.
It would boil down to their degree of plausible deniability, ‘state priviledge’, and the specifics of the law and precedent in their state of course.
Good luck
How that works out in practice is basically you as the owner of the tree have to document it's healthy each year. Then, if it falls and you can prove it was healthy you're fine. Hopefully neighbors insurance pays. If you didn't document the health of the tree, your neighbor can press charges and you (or your insurance) have to pay.
I think I unintentionally brought Tree Law to HN.
Now that I think of this may be the first time that I've seen Tree Law on here.
We're only a hop, skip and a jump from getting some vigorous discussion about Bay area Tree Law now.
What they are noting is the State is it’s own beast, and good luck getting it to do what you want.
This also is not a city type situation, where the density and value of something makes certain types of situations play out differently.
In the city, if a neighbor’s diseased tree falls on your house, you might have a legitimate legal claim, depending on the circumstances.
Your homeowners insurance will figure that out.
If one of the million random trees on state property falls on your fence? It doesn’t much matter what the law says, good luck.