Whenever any city, town, or village has annexed a new site under the provisions of sections 71.016 to 71.019, the legislative body of the city, town, or village may exclude from its boundaries any portion or portions of the territory embraced within its limits as they existed prior to the annexation of the new site whenever by reason of inundation, disoccupation or any other cause whatsoever, the retention thereof within the limits of the city, town, or village ceases to be desirable for the public interest and for the interest of the inhabitants thereof and of the owners of such land. Until such exclusion, all portions of the original territory of the city, town, or village shall continue within its limits and shall be subject to its governmental authority. Proceedings for such exclusion of territory shall be in accordance with the general laws of this state.