  A Black Hole (BH) is a spacetime region with a horizon and where geodesics
converge to a singularity. At such a point, the gravitational field equations
fail. As an alternative to the problem of the singularity arises the existence
of Exotic Compact Objects (ECOs) that prevent the problem of the singularity
through a transition phase of matter once it has crossed the horizon. ECOs are
characterized by a closeness parameter or cutoff, $\epsilon$, which measures
the degree of compactness of the object. This parameter is established as the
difference between the radius of the ECO's surface and the gravitational
radius. Thus, different values of $\epsilon$ correspond to different types of
ECOs. If $\epsilon$ is very big, the ECO behaves more like a star than a black
hole. On the contrary, if $\epsilon$ tends to a very small value, the ECO
behaves like a black hole. It is considered a conceptual model of the origin of
the cutoff for ECOs, when a dust shell contracts gravitationally from an
initial position to near the Schwarzschild radius. This allowed us to find that
the cutoff makes two types of contributions: a classical one governed by
General Relativity and one of a quantum nature, if the ECO is very close to the
horizon, when estimating that the maximum entropy is contained within the
material that composes the shell. Such entropy coincides with the
Bekenstein--Hawking entropy. The established cutoff corresponds to a dynamic
quantity dependent on coordinate time that is measured by a Fiducial Observer
(FIDO). Without knowing the details about quantum gravity, parameter $\epsilon$
is calculated, which, in general, allows distinguishing the ECOs from BHs.
Specifically, a black shell (ECO) is undistinguishable from a BH.
