Lean premixed gas turbulent flames stabilized in the flow generated by an industrial swirl burner with a central bluff body are experimentally found to behave bistable. This bistable behavior, which can be triggered via a small change in some of the controlling parameters, for example, the bulk equivalence ratio, consists in a rather sudden transition of the flame from completely lifted to well attached to the bluff body. This has impact on combustion dynamics, emissions, and pressure losses. While several experimental investigations exist on this topic, numerical analysis is limited. This work is therefore also of numerical nature, with a twofold scope: (a) simulation and validation with experiments of the bistable flame behavior via computational fluid dynamics (CFD) in the form of large eddy simulation (LES) and (b) analysis of CFD results to shed light on the flame stabilization properties. LES results, in case of the lifted flame, show that the vortex core is sharply precessing at a given frequency. Phase averaging these results at the frequency of precession clearly indicates a counterintuitive and unexpected presence of reverse flow going all the way through the flame apex and the bluff body tip. The counterintuitive presence of a lifted flame is explained here in terms of the phase averaged data, which show that the flame apex is not placed at the center of the spinning reverse flow region. It is instead slightly shifted radially outward where the axial velocity recovers to low positive values of the order of the turbulent burning rate. A simple one-dimensional flame stabilization model is applied to explain this peculiar flame behavior. This model provides first an estimation of the flame radius of curvature in terms of axial velocity and turbulence quantities. This radius is therefore used to determine the total flux of reactants into the flame, given by an axial convection and radial diffusion contributions. Subsequently, the possibility of the flame positioned at the center of the vortex is excluded based on the balance between this flux and the turbulent burning rate. A clear explanation of the mechanism leading to the sudden flame jump has instead not been identified and only some hypotheses are provided.