No Contract or Payment on Fence Rental

So I have been renting my house for a year now. I probably should’ve tried to figure this out back when we first moved in, but did not. The house didn’t come with a fence and we had to rent one through a local company. The company came out and installed the fence, but left before they gave us a contract to sign or before we could pay them. We tried calling a few times after, but never got ahold of anyone.

So we will be moving soon and our landlord requires us to get rid of the fence. I’m not sure what to do since I’m afraid the company will come after me for the entire amount owed and honestly I won’t be able to do pay due to some unforeseen circumstances. What is likely to happen in this situation and what are my options?