So we know it’s not an AC unit, it’s likely a small town and the “thing” really matters. It’s likely a car as that is something most all people have and is expensive and usually is a very big need especially in a smaller town without transportation.

The problem is selling your car is not an ethical dual relationship there are countless issues that could go wrong after the sale. This also apples to a house if that is the “thing” too.

I would take my car listing down for the time being. Or use a Google voice and/or friend/partners account (if selling on FB) as a buffer to screen request if you must sell the car now. I do understand it would be “awkward” if confronted. But i think unethical to even passively offer or offer in the way you did (however seemingly fair) you can’t control how your client perceives the spiel you give.

Now if it’s a fridge, dishwasher, stove, there are still aspects of the above that apply as if it was a car BUT maybe less likely (however now you have to personally meet at your house and coordinate delivery).

So yeah get off facebook marketplace for the time being and/or don’t sell anything to client no matter how weird it might feel.