Charge conservation and the Pauli exclusion principle result from fundamental symmetries in the standard model of particle physics, and are typically taken as axiomatic. High-precision tests for small violations of these symmetries could point to new physics. Here we consider three models for violation of these processes, which would produce detectable ionization in the high-purity germanium detectors of the Majorana Demonstrator experiment. Using a 37.5 kg yr exposure, we report a lower limit on the electron mean lifetime, improving the previous best limit for the e→νeνe¯νe decay channel by more than an order of magnitude. We also present searches for two types of violation of the Pauli exclusion principle, setting limits on the probability of an electron to be found in a symmetric quantum state.