Parametrically driven extended systems exhibit dissipative localized states. Analytical solutions of these states are characterized by a uniform phase and a bell-shaped modulus. Recently, a type of dissipative localized state with a nonuniform phase structure has been reported: the phase shielding solitons. Using the parametrically driven and damped nonlinear Schrödinger equation, we investigate the main properties of this kind of solution in one and two dimensions and develop an analytical description for its structure and dynamics. Numerical simulations are consistent with our analytical results, showing good agreement. A numerical exploration conducted in an anisotropic ferromagnetic system in one and two dimensions indicates the presence of phase shielding solitons. The structure of these dissipative solitons is well described also by our analytical results. The presence of corrective higher-order terms is relevant in the description of the observed phase dynamical behavior.