We investigate the parity nonconservation effect in the elastic scattering of polarized electrons on heavy He-like ions, being initially in the ground state. The enhancement of the parity violation is achieved by tuning the energy of the incident electron in resonance with quasidegenerate doubly-excited states of the corresponding Li-like ion.We consider two possible scenarios. In the first one we assume that the polarization of the scattered electron is measured, while in the second one it is not detected.