  Periodic Jacobi operators naturally arise in numerous applications, forming a
cornerstone in various fields. The spectral theory associated with these
operators boasts an extensive body of literature. Considered as discretized
counterparts of Schr\"odinger operators, widely employed in quantum mechanics,
Jacobi operators play a crucial role in mathematical formulations.
  The classical uniqueness result by G. B\"org in $1946$ occupies a significant
place in the literature of inverse spectral theory and its applications. This
result is closely intertwined with M. Kac's renowned article, 'Can one hear the
shape of a drum?' published in $1966$. Since $1975,$ discrete versions of
B\"org's theorem have been available in the literature.
  In this article, we concentrate on the non-normal periodic Jacobi operator
and the discrete versions of B\"org's Theorem. We extend recently obtained
stability results to encompass non-normal cases. The existing stability
findings establish a correlation between the oscillations of the matrix entries
and the size of the spectral gap.
  Our result encompasses the current self-adjoint versions of B\"org's theorem,
including recent quantitative variations. Here, the oscillations of the matrix
entries are linked to the path-connectedness of the pseudospectrum.
Additionally, we explore finite difference approximations of various linear
differential equations as specific applications.
