  We apply the barcodes of persistent homology theory to the
Chekanov-Eliashberg algebra of a Legendrian submanifold to deduce displacement
energy bounds for arbitrary Legendrians. We do not require the full
Chekanov-Eliashberg algebra to admit an augmentation as we linearize the
algebra only below a certain action level. As an application we show that it is
not possible to $C^0$-approximate a stabilized Legendrian by a Legendrian that
admits an augmentation.
