  The destruction of the black-hole event horizon is ruled out by both cosmic
censorship and the generalized second law of thermodynamics. We test the
consistency of this prediction in a (more) `dangerous' version of the gedanken
experiment suggested by Bekenstein and Rosenzweig. A U(1)-charged particle is
lowered {\it slowly} into a near extremal black hole which is not endowed with
a U(1) gauge field. The energy delivered to the black hole can be {\it
red-shifted} by letting the assimilation point approach the black-hole horizon.
At first sight, therefore, the particle is not hindered from entering the black
hole and removing its horizon. However, we show that this dangerous situation
is excluded by a combination of {\it two} factors not considered in former
gedanken experiments: the effect of the spacetime curvature on the
electrostatic {\it self-interaction} of the charged system (the black-hole
polarization), and the {\it finite} size of the charged body.
