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It's pretty straightforward. Neutrons are fermions and as such
two neutrons cannot occupy the same quantum mechanical state
in a nucleus. When all of the energetically bound quantum
states in a nucleus are occupied by neutrons, the next neutron
in must go into a higher (and therefor unbound) energy state.
Of course it will come right out, there being no barrier high
enough to hold it in.
The same mechanism operates in building up the electron shells
around the nucleus of an atom. There is a shell model of the
nucleus as well, largely due to Maria Goepert Mayer. That is
the model in which this explanation is most intuitively seen
to operate.
I'll add one more thing. It turns out that in the case of the
hydrogen atom in its ground state, it is possible to add one
more bound electron. The resulting object, the H- ion, is the
species principally responsible for the opacity of the Sun.
Does that help?
Leigh