As was shown by N. Engheta, electromagnetic fields in two adjacent slabs bounded by two metal walls can satisfy the boundary conditions even if the distance between the two walls is much smaller than the wavelength. This is possible if one of the slabs has a negative permeability. Here we show that these subwavelength "resonators" resonate only if the permeability of at least one of the slabs is frequency dependent. Thus, there is no advantage of using these structures with "left-handed" slabs as frequency-selective devices. However, we have found that these systems can be in principle used as memory devices for evanescent fields, because the boundary conditions are identically satisfied for all plane evanescent waves inside the cavity. The physical meaning and practical limitations for possible realizations are discussed. The analysis is supported by FDTD simulations.