In general, if the settlement is not more that the value of your old fence, then it is not taxable.
The IRS says:
Loss-in-value of property
Property settlements for loss in value of property that are less than the adjusted basis of your property are not taxable and generally do not need to be reported on your tax return. However, you must reduce your basis in the property by the amount of the settlement.
If the property settlement exceeds your adjusted basis in the property, the excess is income. For more information, see the Instructions for Schedule D, (Form 1040) Capital Gains and Losses and the Instructions for Form 4797, Sales of Business Property.
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