We address the origin of the magnetic-field independent -|A| T^{1/2} term observed in the low-temperature resistivity of several As-based metallic systems of the PbFCl structure type. For the layered compound ZrAs_{1.58}Se_{0.39}, we show that vacancies in the square nets of As give rise to the low-temperature transport anomaly over a wide temperature regime of almost two decades in temperature. This low-temperature behavior is in line with the non-magnetic version of the two-channel Kondo effect, whose origin we ascribe to a dynamic Jahn-Teller effect operating at the vacancy-carrying As layer with a C_4 symmetry. The pair-breaking nature of the dynamical defects in the square nets of As explains the low superconducting transition temperature T_{rm{c}}approx 0.14 K of ZrAs_{1.58}Se_{0.39}, as compared to the free-of-vacancies homologue ZrP_{1.54}S_{0.46} (T_{rm{c}}approx 3.7 K). Our findings should be relevant to a wide class of metals with disordered pnictogen layers.
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