  We unveil a new scenario for the formation of dissipative localised
structures in nonlinear systems. Commonly, the formation of such structures
arises from the connection of a homogeneous steady state with either another
homogeneous solution or a pattern. Both scenarios, typically found in cavities
with normal and anomalous dispersion, respectively, exhibit unique fingerprints
and particular features that characterise their behaviour. However, we show
that the introduction of a periodic non-Hermitian modulation in Kerr cavities
hybridises the two established soliton formation mechanisms, embodying the
particular fingerprints of both. In the resulting novel scenario, the
stationary states acquire a dual behaviour, playing the role that was
unambiguously attributed to either homogeneous states or patterns. These
fundamental findings have profound practical implications for frequency comb
generation, introducing unprecedented reversible mechanisms for real-time
manipulation.
