  In gravitational collapse leading to black hole formation, trapping horizons
typically develop inside the contracting matter. Classically, an ingoing
trapping horizon moves towards the centre where it reaches a curvature
singularity, while an outgoing horizon moves towards the surface of the star
where it becomes an isolated, null horizon. However, strong quantum effects at
high curvature close to the centre could modify the classical picture
substantially, e.g. by deflecting the ingoing horizon to larger radii, until it
eventually reunites with the outgoing horizon. We here analyse some existing
models of regular "black holes" of finite lifespan formed out of ingoing null
shells collapsing from $\mathscr{I}^-$, after giving general conditions for the
existence of (singularity-free) closed trapping horizons. We study the
energy-momentum tensor of such models by solving Einstein's equations in
reverse and give an explicit form of the metric to model a Hawking radiation
reaching $\mathscr{I}^+$. A major flaw of the models aiming at describing the
formation of black holes (with a Vaidya limit on $\mathscr{I}^-$) as well as
their evaporation is finally exhibited: they necessarily violate the null
energy condition up to $\mathscr{I}^-$, i.e. in a non-compact region of
spacetime.
