This　paper　investigates　the　global　existence　and　asymptotic　behavior　of　solutions　to　the　system　of　an　incompressible,　inviscid,　non-resistive　magnetohydrodynamic　(MHD)　fluid　with　a　velocity　damping　term　in　a　two-dimensional　(2D)　horizontally　periodic　domain,　analyzed　in　Lagrangian　coordinates.　Motivated　by　the　oddity　conditions　introduced　in　Pan　et　al.　(2018)　[16],　we　establish　the　global　existence　of　a　unique　classical　solution　for　some　class　of　large　initial　perturbations　correlated　with　the　intensity　of　the　impressed　magnetic　field.　Furthermore,　we　demonstrate　that　the　solution　exhibits　exponential　decay　in　time　towards　its　equilibrium.　Additionally,　we　show　that　for　large　times　or　sufficiently　strong　impressed　magnetic　fields,　the　nonlinear　MHD　system　converges　to　the　corresponding　linearized　problem,　with　convergence　rates　that　are　algebraic　in　the　magnetic　field　strength　and　exponential　in　time.　©　2025　Elsevier　Inc.