The prospect of stabilization of the m = 1 "rigid" ballooning regime in an open axially symmetric trap with the help of a conducting lateral wall surrounding a column of isotropic plasma is studied. It is found that for effective wall stabilization, the beta parameter must exceed 70%. The dependence of the critical value of beta on the mirror ratio, the radial pressure profile, and the axial profile of the vacuum magnet has been studied. It is shown that when a conductive lateral wall is combined with conductive ends simulating the attachment of end MHD stabilizers to the central cell of an open trap, there are two critical beta values and two stability zones that can merge, making stable the entire range of allowable beta values 0 < β < 1.