  It has been shown recently that quark-hadron conversions at the interface of
a hybrid star may have a key role on the dynamic stability of the compact
object. In this work we perform a systematic study of hybrid stars with
reactive interfaces using a model-agnostic piecewise-polytropic hadronic
equation of state and the Nambu-Jona-Lasinio model for three-flavor quark
matter. For the hadronic phase we use a soft, an intermediate and a stiff
parametrization that match at $1.1 n_0$ {with predictions} based on chiral
effective field theory (cEFT) interactions. In the NJL Lagrangian we include
scalar, vector and 't Hooft interactions. The vector coupling constant $g_{v}$
is treated as a free parameter. We also consider that there is a split between
the deconfinement and the chiral phase transitions which is controlled by
changing the conventional value of the vacuum pressure $-\Omega_{0}$ in the NJL
thermodynamic potential by $-\left(\Omega_{0}+\delta \Omega_{0}\right)$, being
$\delta \Omega_{0}$ a free parameter. We analyze the mass-radius ($M$-$R$)
relation in the case of rapid ($\tau \ll 1 \, \mathrm{ms}$) and slow ($\tau \gg
1 \, \mathrm{ms}$) conversions, being $\tau$ the reaction timescale. In the
case of slow interface reactions we find $M$-$R$ curves with a cusp at the
maximum mass point where a pure hadronic branch and a slow-stable hybrid star
(SSHS) branch coincide. We find that the length of the slow-stable branch grows
with the increase of the transition density and the energy density jump at the
hadron-quark interface. We calculate the tidal deformabilities of SSHSs and
analyse them in the light of the GW170817 event.
