  The concept of the irreducible mass ($M_{\rm irr}$) has led to the
mass-energy ($M$) formula of a Kerr-Newman black hole (BH), in turn leading to
an expression for its surface area $S=16\pi M_{\rm irr}^2$. This allowed as
well the coeval identification of the reversible and irreversible
transformations. The concepts of \textit{extracted} and \textit{extractable}
energy soon followed. This new conceptual framework avoids inconsistencies
recently evidenced in a repetitive Penrose process. We consider repetitive
decays in the ergosphere of an initially extreme Kerr BH and show that these
processes are highly irreversible. For each decay, including the BH capture of
the particle falling into the horizon, the increase of the irreducible mass is
much larger than the extracted energy. Correspondingly, the horizon radius
increases. The energy extraction process saturates and stops when the horizon
reaches the decay radius. Thus, reaching a final non-rotating Schwarzschild BH
state by this accretion process is impossible. We have assessed such processes
for three selected decay radii, $r= 1.2 M$, $1.5 M$, and $1.9 M$. The energy
extracted until saturation is only $2.75\%$, $4.54\%$, and $2.45\%$ of the BH
initial mass, while the extractable energy is reduced by $25\%$, $56\%$, and
$92\%$. The BH rotational energy is mostly converted into irreducible mass,
which increases to $75\%$, $83\%$, and $95\%$ of the initial BH mass.
Therefore, evaluating the effect of the irreducible mass increase in the energy
extraction processes in the Kerr BH ergosphere is now mandatory.
