  Charge conservation and the Pauli exclusion principle (PEP) result from
fundamental symmetries in the Standard Model, and are typically taken as
axiomatic. High-precision tests for small violations of these symmetries could
point to new physics. In this work we consider three models for violation of
these processes which would produce detectable ionization in the high-purity
germanium detectors of the Majorana Demonstrator. Using a 37.5 kg-yr exposure,
we report a new lower limit on the electron mean lifetime of $\tau_e > 3.2
\times 10^{25}$ yr (90\% CL), the best result for this decay channel ($e
\rightarrow \nu_e \overline{\nu_e} \nu_e$ or more generally $e \rightarrow
\mathrm{invisibles}$) in more than two decades. We also present searches for
two types of violation of the PEP, setting new limits on the probability of two
electrons forming a symmetric quantum state. Using our $^{228}$Th calibration
data set, which introduces electrons new to the system through
electron-positron pair production, we obtain a world-leading model-independent
limit for a terrestrial experiment of $\beta^2/2 < 1.0 \times 10^{-3}$ (99.7\%
CL). Our 37.5 kg-yr exposure is also used to search for a process where an
electron in an atomic system spontaneously violates the PEP, resulting in a
model-dependent upper limit of $\beta^2/2 < 1.0 \times 10^{-48}$ (90\% CL).
