  Tests of the weak cosmic censorship conjecture examine the possibility of the
breakdown of predictivity of the gravitational theory considered, by checking
if curvature singularities typically present in black hole spacetimes are
concealed within an event horizon at all times. A possible method to perform
such tests was proposed by Wald and consists in trying to overspin an extremal
rotating black hole by throwing at it a test particle with large angular
momentum. In this paper, we analyze the effects of dropping a test particle
into an extremal quantum rotating BTZ black hole, whose three-dimensional
metric captures the exact backreaction from strongly coupled quantum conformal
fields. Our analysis reveals that, despite the inclusion of quantum effects,
and akin to the classical scenario, these attempts to destroy the black hole
are doomed to be unsuccessful. Particles carrying the maximum angular momentum
and still falling into an extremal quantum BTZ black hole can, at most, leave
it extremal. Nevertheless, we found numerical evidence that large backreaction
of the quantum fields tends to disfavor violations of cosmic censorship.
