In case any proprietor of land shall improve his or her land, the land adjoining being unimproved, and shall make the whole partition fence, the proprietor or possessor of the land adjoining and unimproved shall, upon improvement thereof, pay for one-half (½) of the partition fence, according to the value thereof at that time, and shall keep up and maintain the same ever afterwards, whether he or she shall continue to improve the land or not.