Features of Penning ionization in cold gaseous media of Rydberg alkali-metal atoms have been investigated. In contrast to the hydrogen atom, the corresponding autoionization widths exhibit a strong (by orders of magnitude) dependence on the orbital quantum numbers of the atoms involved in the long-range dipole-dipole interaction. An important feature of Penning ionization is the nontrivial dependence of its efficiency on the Rydberg particle size. For all types of alkali-metal atoms, the optimal highly nonsymmetric configurations of Rydberg pairs have been found that lead to the explosive (by several orders of magnitude) intensification of the free electron formation by means of the Penning ionization processes. This property makes Penning ionization an important means of forming primary charged particles during the cold Rydberg plasma formation. The numerical data for pairs of potassium atoms are reported that demonstrate a significant effect of the Forster resonance on the values of the Penning ionization rate constants.