  Through a semi-analytic approach of the Kozai resonance inside an MMR, we
show phase diagrams (e,{\omega}) that suggest the possibility of a scattered
particle, after being captured in an MMR with Neptune, to become a detached
object. We ran several numerical integrations with thousands of particles
perturbed by the four major planets, and there are cases with and without
Neptune's residual migration. These were developed to check the semi-analytic
approach and to better understand the dynamical mechanisms that produce the
detached objects close to an MMR. The numerical simulations with and without a
residual migration for Neptune stress the importance of a particular resonance
mode, which we name the hibernating mode, on the formation of fossilized
detached objects close to MMRs. When considering Neptune's residual migration
we are able to show the formation of detached orbits. These objects are
fossilized and cannot be trapped in the MMRs again. We find a ratio of the
number of fossilized objects with moderate perihelion distance (35 < q < 40 au)
to the number of objects with high perihelion distance (q > 40 au) as 3.0/1 for
objects close to the 2:5, and 1.7/1 for objects close to the 1:3 resonance. We
estimate that the two fossilized population have a total mass between 0.1 and
0.3 Pluto's mass.
