By means of 3D particle dynamics simulations, we analyze the microstructure of granular materials subjected to isochoric (constant volume) cyclic shearing, which drives the system towards a liquefaction state characterized by loops of jamming-unjamming transition with periodic loss of strength and irreversible accumulation of shear strain. We first show that the macroscopic response obtained by these simulations agrees well with the most salient features of the well-known cyclic behavior of granular materials both before and after liquefaction. Then we investigate the evolution of particle connectivity, force transmission, and anisotropies of contact and force networks. The onset of liquefaction is marked by partial collapse of the force-bearing network with rapid drop of the coordination number and nonrattler fraction of particles, and significant broadening of the contact force probability density function, which begins in the preliquefaction period. We find that the jamming transition in each cycle occurs for a critical value of the coordination number that can be interpreted as the percolation threshold of the contact network and appears to be independent of the initial mean stress, void ratio, and cyclic shear amplitude. We show that upon unjamming in each cycle an isotropic loss of contacts occurs and is followed by the development of high contact anisotropy and a large proportion of particles with only two or three contacts. The higher mobility of the particles also involves a lower degree of frustration of particle rotations and thus lower friction mobilization and tangential force anisotropy. These findings are relevant to both undrained cyclic deformations of saturated soils and rheology of dense non-Brownian suspensions where volume change is coupled with pore liquid drainage conditions.