I was struck by the way in which a cold neutrino star resembles a slowly evaporating black hole. The neutral-current (Z boson) interactions between the neutrinos should lead to a very slow production rate of other particle species, and when charged particles recombine as a photon, it will radiate away. It reminds me of Hawking radiation.
So now I am wondering just how far the resemblance goes. Could the end-state of gravitational collapse be a cold gas of fermions, held apart by Pauli exclusion, and dominated by the fermion species that interacts the least? I'm not sure how to think about the event horizon in this picture, but maybe the "fuzzball" hypothesis applies.
edit: Another thing that struck me, is that falling into a cold neutrino star is like crossing the event horizon of a large black hole; nothing happens at first, because interactions are so weak. So it simulates the equivalence principle at the horizon, yet also has an enormous entropy.