I thought the same but do they care enough about to claim it and have to pay the fee. Those can get pricey and can / will the neighbors/ owners come claim it. If not... what happens to it? They're not easily adopted I know that's not OP problem but sounds like they careUsually there is some agency you can call about trespassing livestock. In some areas it is the sheriff's department and in others it is animal control. I have known of cases where the authorities have impounded the trespassing critter and then taken it to the sales yard where the owner can claim it after paying fees.
I feel so terrible for OP being stuck in this situation !