The coarsening behavior of individual Pb islands on Si(111) surface has been studied by scanning tunneling microscopy. Traditionally island decay follows a smooth power-law dependence on the time until disappearance. In Pb/Si(111), some unstable islands are inactive for a long time but once their decay is triggered they suffer a “sudden death.” Four-layer islands are found to decay rapidly, increasing the area covered by seven-layer islands. All islands, decaying or otherwise, are accompanied by island size fluctuation which involve a large number of perimeter atoms moving collectively as a “quantized” unit. A stochastic model is developed to elucidate the mechanism behind this coarsening behavior of Pb islands. The distinct evolution of the islands with different heights is correctly predicted, and the size fluctuations of islands and the sudden death behavior observed in island coarsening are also recovered. The key ingredients are incorporation of accurate non-Gaussian statistics of the size fluctuations and also accounting for size changes in large quantized bursts.