My question involves real estate located in the State of: Arkansas (Little Rock)
We have a neighbor renting out a home behind ours that shares a fence (we don't know what property line it is on yet). They contacted me a week and a half ago to see if we would fix it or go in on fixing it with them. I told them I would have to talk to my husband first, and gave them no definitive answer. After my husband and I talked it over, we decided to try and fix it ourselves. I called the owners and got permission to go into the yard in an attempt to repair it. When we got there, it was obvious we could not. A former tenant's dog had basically destroyed it. While we were trying to figure out what to do, they took it upon themselves to tear it down, rebuild it, and enter our yard without our consent (and also cut down a crepe myrtle). They also left a voicemail asking for half the costs even though we did not agree to this, and we do not know what property line it is on.
My question for the experts is this: should we be responsible for half the costs? I don't understand why they think it is our responsibility. They brought up the option of splitting the cost when I met them, but NEVER agreed to it. When I got permission to enter their yard, I told them we could try to come up with another solution together if our repairs weren't suitable, but that is as close as I got to agreeing to pay for costs...
I understand that if it is a shared property line, we may be liable for half the cost, but what if it is not? And shouldn't we have been able to agree to the estimate first? We really are not in a position to pay that figure.
Thank you for the help!

