Cohesive granular matter can support stable void structures, which can universally be found in various scenes from everyday lives to space. To quantitatively characterize the stability and strength of a void structure in cohesive granular matter, we perform a simple tunnel-compression experiment with wet granular matter. In the experiment, a horizontal tunnel in a wet granular layer is vertically compressed with a slow compression rate. The experimental result suggests that the tunnel deformation can be classified into the following three types: (i) shrink, (ii) shrink with collapse, and (iii) subsidence by collapse. Using the experimental result, we estimate the stable limit of various void structures in a cohesive granular layer from crab burrows on a sandy beach to the pits observed on cometary surfaces.