In stable environments, cell size fluctuations are thought to be governed by simple physical principles, as suggested by recent findings of scaling properties. Here, by developing a novel microfluidic device and using E. coli, we investigate the response of cell size fluctuations against starvation. By abruptly switching to non-nutritious medium, we find that the cell size distribution changes but satisfies scale invariance: the rescaled distribution is kept unchanged and determined by the growth condition before starvation. These findings are underpinned by a model based on cell growth and cell cycle. Further, we numerically determine the range of validity of the scale invariance over various characteristic times of the starvation process. Combining theory and simulations, we reveal the number of multifork replications is crucial for the scale invariance. Our results emphasize the importance of intrinsic cellular cycle processes in this problem, suggesting different distribution trends for bacteria and eukaryotes.