  The nature of the Fermi surface observed in the recently discovered family of
unconventional insulators starting with SmB$_6$ and subsequently YbB$_{12}$ is
a subject of intense inquiry. Here we shed light on this question by comparing
quantum oscillations between the high magnetic field-induced metallic regime in
YbB$_{12}$ and the unconventional insulating regime. In the field-induced
metallic regime beyond 47 T, we find prominent quantum oscillations in the
contactless resistivity characterised by multiple frequencies up to at least
3000 T and heavy effective masses up to at least 17 $m_\text{e}$,
characteristic of an $f$-electron hybridised metallic Fermi surface. The growth
of quantum oscillation amplitude at low temperatures in electrical transport
and magnetic torque in insulating YbB$_{12}$ is closely similar to the
Lifshitz-Kosevich low temperature growth of quantum oscillation amplitude in
field-induced metallic YbB$_{12}$, pointing to an origin of quantum
oscillations in insulating YbB$_{12}$ from in-gap neutral low energy
excitations. The field-induced metallic regime of YbB$_{12}$ is characterised
by more Fermi surface sheets of heavy quasiparticle effective mass that emerge
in addition to the heavy Fermi surface sheets yielding multiple quantum
oscillation frequencies below 1000 T observed in both insulating and metallic
regimes. We thus observe a heavy multi-component Fermi surface in which
$f$-electron hybridisation persists from the unconventional insulating to the
field-induced metallic regime of YbB$_{12}$, which is in distinct contrast to
the unhybridised conduction electron Fermi surface observed in the case of the
unconventional insulator SmB$_6$. Our findings require a different theoretical
model of neutral in-gap low energy excitations in which the $f$-electron
hybridisation is retained in the case of the unconventional insulator
YbB$_{12}$.
