Often urbanists discuss the growth of cities in the context of increasing density and the vertical scale of cities. But rarely is the growth of cities discussed in the realm of the political boundary. To get the ball rolling here is a video on the geographic growth of Houston:
As you can see, Houston grew politically larger during the era when many cities shrank in population and ceased their political growth.
For comparison here is a map of Chicago's annexation. There is an animated gif of Chicago's growth HERE. As you can see, Chicago stopped growing its political boundary in the 1950s. Another point of contrast is the Detroit annexation map, which is available HERE. There is also an animated version:
Curiously Detroit ceased its political growth in the 1920s. If cities like Detroit and Chicago continued to annex the peripheral neighborhoods these cities would have had no population declines.