  We study here the gravitational collapse of dust in $(2+1)$-dimensional
spacetimes for the formation of black holes (BH) and naked singularities (NS)
as final states in a modified theory of gravity, with vanishing cosmological
constant. From the perspective of cosmic censorship, we investigate the
collapse of a dust cloud in Eddington-inspired Born-Infeld gravity (EiBI) and
compare the results with those of general relativity (GR). It turns out that,
as opposed to the general relativistic situation, where the outcome of dust
collapse in $(2+1)$ dimensions is always a naked singularity, the EiBI theory
has a certain range of parameter values that avoid the naked singularity. This
indicates that a $(3+1)$-dimensional generalization of these results could be
useful and worth examining. Finally, using the results here, we show that the
singularity avoidance through homogeneous bounce in cosmology in this modified
gravity is not stable.
