Pauli Exclusion and Black Holes Pauli exclusion principle states that 2 identical electrons cannot be in the same state, where state includes a spacial component. 
I have heard that, in order to avoid being in the same state, in a white dwarf, the De Broglie wave length of the electrons becomes shorter and shorter, meaning that they have a higher and higher momentum/ energy. Eventually, when the gravitational pressure is too high, they form neutron stars, since neutrons have smaller De Broglie Wave lengths due to their higher mass.
My question is, by applying more and more pressure, can we confine more and more identical neutrons/ other fermions in an arbitrarily small space, eventually forming a black hole? Or, at some point, fermions must be converted into bosons?
 A: 
My question is, by applying more and more pressure, can we confine more and more identical neutrons/ other fermions in an arbitrarily small space, eventually forming a black hole? Or, at some point, fermions must be converted into bosons?

Black holes are classical entities.Fermions and bosons are quantum  mechanical entities. Questions that mix the two frames will not have a definite answer until/when gravity is quantized.
In the standard model, fermions can couple up and become bosons, as for example pions are made up out of two fermions, a quark and an antiquark. So this could be a hypothesis in some specific quantization model. 
At the moment cosmological models work with effective quantization of gravity, which replaces the point singularities into a fuzzy quantum mechanical region. In such a region it is not forbidden to keep the logic of higher and higher energy for the energy carriers, in your question fermions, because there is no limit to how many energy levels there can be in the fuzzy quantum mechanical region, as for example at the beginning of the Big Bang, and thus be able to fulfill the Pauli exclusion.
