It's fairly easy to show based on basic ideas of quantum mechanics that the most stable form of nuclear matter (for small A) has N and Z approximately equal. The reason is simply the Pauli exclusion principle. If I have 8 protons and 8 neutrons, I can put the 8 protons in the lowest 8 energy levels, and the 8 neutrons in the lowest 8 energy levels. If I have 16 neutrons and no protons, then the first 8 neutrons can go in the lowest 8 energy levels, and the next 8 have to go in the next 8 levels, with higher energies. That's enough to show that N=16, Z=0 isn't going to be a stable system. At best, it might beta decay to 16O.
There's also the question of whether these systems would even be bound with respect to particle emission, in which case they could only be observed as resonances. Since there is no Coulomb barrier for neutrons, they don't have to tunnel out. If they've got enough energy to escape, they just do. Then it becomes a question of the strength of the nuclear force. The best experimental and theoretical work so far seems to show that N=2 is unbound, and N=6, 8, 10, ... are also pretty clearly unbound. There is still at least some question whether N=4 is bound.
These people claimed to have detected the N=4 system, with a lifetime of at least ~100 ns, which means it would have to be bound, although not stable with respect to beta decay:
http://arxiv.org/abs/nucl-ex/0111001
Whether they're right is a whole different question. I wouldn't bet a six-pack on it.