Young stellar bars in disk galaxies experience a vertical buckling instability that terminates their growth and thickens them, resulting in a characteristic peanut/boxy shape when viewed edge-on. Using N-body simulations of galactic disks embedded in live halos, we have analyzed the bar structure throughout this instability and found that the outer (approximately) third of the bar dissolves completely while the inner part (within the vertical inner Lindblad resonance) becomes less oval. The bar acquires the frequently observed peanut/boxy-shaped isophotes. We also find that the bar buckling is responsible for a mass injection above the plane, which is subsequently trapped by specific three-dimensional families of periodic orbits of particular shapes explaining the observed isophotes, in line with previous work. Using a three-dimensional orbit analysis and surfaces of sections, we infer that the outer part of the bar is dissolved by a rapidly widening stochastic region around its corotation radius-a process related to the bar growth. This leads to a dramatic decrease in the bar size, decrease in the overall bar strength, and a mild increase in its pattern speed but is not expected to lead to a complete bar dissolution. The buckling instability appears primarily responsible for shortening the secular diffusion timescale to a dynamical one when building the boxy isophotes. The sufficiently long timescale of the described evolution, ~1 Gyr, can affect the observed bar fraction in the local universe and at higher redshifts, both through reduced bar strength and the absence of dust offset lanes in the bar.