The wall-resolved large-eddy simulation (WRLES) database of the flow around the A-airfoil at the near-stall condition [K. Asada and S. Kawai, Phys. Fluids 30, 085103 (2018)PHFLE61070-663110.1063/1.5037278] is analyzed to understand the mechanism of the boundary layer development and to examine the predictability of the trailing-edge stall phenomena using the wall-modeled LES (WMLES). The analysis based on the integral relation for the boundary layer indicates that the skin friction has dominant effects on the boundary layer development in the mild-adverse pressure gradient region (x/c>0.6). The effects of the skin friction accumulate along the airfoil upper surface, which determines the growth of the momentum thickness in the downstream and the consequent flow separation near the trailing edge. Therefore, this analysis indicates that the wall modeling in x/c<0.6 is important for the prediction of the stall phenomena, while that near and downstream of the separation location little affects the stall phenomena. Also, the budget analysis reveals that the eddy viscosity in the mild-adverse pressure gradient regions increases compared to that of the equilibrium boundary layer, which should be incorporated properly in the wall model. The same flowfield is simulated using the WMLES, and the results show an overall good agreement with the WRLES. The analysis based on the integral relation indicates that the WMLES can predict the stall phenomena with reasonable accuracy because the outer layer turbulence, whose effects are dominant near the separation point, is directly resolved in the WMLES. Despite the overall agreement with the WRLES, the WMLES results also suggest that potential issues remain in the underresolution near the leading edge and the eddy viscosity modeling of the wall model for flows with adverse pressure gradient.