  By neglecting the effects of self-force and radiation, we investigate the
possibility of destroying the Kerr-MOG black hole through the point particle
absorption process. Using the instability of event horizon and equation of
particle motion, we get the upper and lower energy bounds allowed for a matter
particle to produce the naked singularity. We find that the energy gap always
exists between the upper and lower energy bounds for both extremal and
near-extremal black holes, which means some tailored particles can actually
lead to the violation of the weak cosmic censorship conjecture. However, when
considering the effect of the adiabatic process, the result shows that the
Kerr-MOG black hole gets more stable instead of a naked singularity, and thus
the weak cosmic censorship conjecture can be restored at some level.
