Electrons have always some kinetic energy, it is requirement of QM principles. Plus there is distribution of the threshold photon energy due Doppler effect, because of moving atoms. Near stationary electrons will probably attach themselves back to the solid matrix, possibly leading to local charge disbalance. We are already used to that in static electricity context.
In the above scenario, electron will have like thermal speed when released. what for low electron mass and 298 K is typically $v_\mathrm{RMS}=\sqrt(\frac{3kT}{m_\mathrm{e}}) \approx \pu{116 km/s}$.
For mettallic conductors with metallic bonds, where electrons can freely move, one electron less or more as the structure deviation play no significant role, similarly as electrons and "holes" in semiconductors.
For covalent bond structures, electrons as point charges will tend to bind to many neutral molecules, forming anions. It is similar to "naked" protons.
Near all elements (but noble gases and few exceptions) have positive electron affinity is spite of dense clouds of electrons around their nucleus. It should not be therefore surprising electrons can attach itself to molecules.
An electron can also return to its original place while releasing its energy, or to break a bond and attach to one of fragments.
E.g.:
$$\ce{e- + R3C-H -> R3C- + H^.}$$
or
$$\ce{e- + R3C-OH -> R3C^. + OH-}$$
