An azimuthally continuous conducting wall cannot be used to provide stabilization for time-dependent magnetic confinement fields, such as the recently proposed traveling, compressing mirror [P. M. Bellan, Phys. Rev. Lett. 43, 858 (1979)], because, unlike static confinement fields, time-dependent confinement fields cannot penetrate such a wall. If the wall has a gap, then time-dependent fields can penetrate, but the gap produces an azimuthal asymmetry of the field which can cause enhanced particle losses. By splitting the wall into a large number of short insulated axial sections, each with a randomly oriented azimuthal gap, (i) the time-dependent confining field can penetrate the wall, (ii) wall stabilization is obtained, and (iii) azimuthal symmetry is maintained.