If any horse, mule or ass, or any neat cattle, hogs or sheep, or other domestic animals, shall break into any person’s inclosure, the fence being good and sufficient, the owner of such animal or animals shall be liable, in a civil action, to make good all damages to the owner or occupier of the inclosure. This section shall not be construed to require such fence, in order to maintain an action for injuries done by animals running at large contrary to law.