In case of the burial of a person not having known estate, and not having a suitable marker or headstone erected at his or her grave within three years from the date of such burial, the selectboard of the town or the aldermen of a city, as the case may be, wherein such person is buried, shall cause to be erected at such person's grave, at the expense of such town or city, a suitable marker or headstone with the inscription thereon of the name of the deceased and dates of his or her birth and death, if the same are known.