In the first part of this study we described the process of destabilization of foam films by mixed (silica-silicone oil) antifoam drops as observed with a high-speed video camera. The drops formed oil bridges, which stretched with time and eventually ruptured the foam films. Remarkably, two types of bridges could be distinguished: (i) mechanically unstable ones, which stretched and ruptured the films within several milliseconds, and (ii) metastable ones, that existed for a much longer period (up to several seconds). The stability of oil bridges is theoretically analyzed in the current article, which presents a further development of the model by Garrett (J. Colloid Interface Sci. 1980, 76, 587). The deformation of the foam film surfaces, which was previously neglected, is explicitly taken into account. The effect of several governing factors (three-phase contact angles, film thickness, size of the bridge, presence of spread oil layer) on the evolution and stability of the oil bridges is analyzed. The calculations show that the bridge stability depends primarily on two factors: (i) the contact angle oil-water-air and (ii) the relative size of the bridge (with respect to the film thickness). Mechanically stable bridges can be formed at any value of the three-phase contact angle if the relative size of the bridge is below a given critical value. Above the critical size, the bridge stability is determined by the contact angle (i.e., by the corresponding bridging coefficient B, as introduced by Garrett). The reduced stability of the bridges in the presence of a prespread oil layer is explained by an accumulation of oil in the bridge (from the spread layer), which leads to an actual increase of the size of the bridge. The theoretical predictions are compared with the experimental results and are discussed from the viewpoint of the mechanisms of antifoam action.