  Sine-Gordon deformed defects that exhibit unusual phenomenological features
on the topological charge are investigated. The possibility of a smooth and
continuous transition between topological (non null charge) and non-topological
(null charge) scenarios of deformed defects supported by sine-Gordon structures
is evinced by the analytical calculation of topological charges and localized
energy distributions. By describing cyclic deformation chains, we show that a
triggering sine-Gordon model simultaneously supports kink and lump-like
defects, whose topological mass values are closed by trigonometric or
hyperbolic successive deformations. In spite of preserving analytical closure
relations constraining the topological masses of $3$-and $4$-cyclically
deformed defects, the deformation chains produce kinks and lumps which exhibit
non-monotonic behavior and extra inflection points, respectively. The outcome
of our analysis suggests that cyclic deformations create novel scenarios of
physical and mathematical applicability of defect structures supported by the
sine-Gordon theory.
