The truncated geometry of the liquid-solid interface in Si, Ge, and zincblende III-V nanowires grown by the vapor-liquid-solid method has far-reaching implications in the nanowire morphology, crystal phase, and doping process. It has previously been found that the amount of truncation oscillates in synchronization with the monolayer growth cycle, which was explained within a model of Tersoff and coauthors. Here, we develop an advanced model for the oscillations of the truncated geometry in vapor-liquid-solid nanowires and study in detail different stages of monolayer growth in nanowires with such a geometry. It is shown that the large truncated volumes (on the order of one monolayer) observed experimentally in different nanowires are due to the stopping effect upon reaching zero supersaturation in a catalyst droplet. This effect is specific for small droplets, which do not contain enough material at nucleation to grow a whole monolayer from liquid. Upon reaching zero supersaturation of the liquid phase, the monolayer growth rapidly continues by taking the required amount of material from the truncation, which explains the rapid increase in the truncated volume after the stopping size. In growth conditions without a stopping size, the calculated truncation volumes are much smaller and may be even unphysically small for GaAs and other III-V nanowires. The model is applied to self-catalyzed zincblende GaAs nanowires and Au-catalyzed Si nanowires and compared to the available experimental data.