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I don't understand your thinking...
The fence is ruined.
It's neither yours, nor the person your buying off's responsibility to pay to repair it.
You want the people you're buying off to pay half the cost to replace the fence that's legally not theirs.
You feel their not doing so are grounds to reopen discussion on agreed price of purchase.
You're quibbling over sub 1k worth of work on what I guess is a 500K+ purchase.
So it seems that we will be getting a house with a ruinous (RH) garden fence. The lawyer’s paperwork show it actually is the neighbours responsibility. Is there any way (other than offering £££ got partial or total replacement) to get the current owners them to replace or at least have a chat with the said neighbors?