You are right. The nucleons are inside nucleus. The decay proceeds in many-body environment. That's the main point  giving the grounds for quasi-particle picture, shell-model,  pnQRPA e.t.c. Your observation: " I definitely know that inside the nucleus when neutrons are at the inner shells they don't decay "  is  true when (beta-unstable) nuclei are still relatively close to the beta- stability line. But the main criteria for beta-decay is always the same: positive decay Q value. Thus, a decay condition is defined by the relative energies of the combined neutron and proton quasi-particles. How different are the main oscillator numbers of the shells in which they are sitting  depends, of course on N/Z ratio. In the most neutron-rich  region of nuclear chart near the 78Ni, the decays from the completely filled neutron shell are experimentally known. Example:  Ga isotopes with N>50 ( their  half-lives measured up to N=55. Physical Review Letters, 2012, v. 109, 112501. ). One can find there both the  Gamow-Teller decays from filled N=50 shell and first-forbidden decays from partially filled N=56 sub-shell. They give a competing contributions to the total half-lives. Also the delayed one-neutron and even two-neutron  emission is possible in these nuclei. That is it about the beta-decay of the neutrons inside the nucleus.  What Shad B. mentioned is for the direct particle-decay channel. For that we have to go to the neutron drip-line nuclei. Still in these hypothetical species we will also find the beta-decay from the filled N-shells. Look e.g to doubly-magic 176Sn which seems to be  particle-bound system (at least in some versions of energy-density functionals).

It depend on the binding energy of the that particular valence neutron. If the binding energy is week then the neutron will emitted. 

You are right. The nucleons are inside nucleus. The decay proceeds in many-body environment. That's the main point  giving the grounds for quasi-particle picture, shell-model,  pnQRPA e.t.c. Your observation: " I definitely know that inside the nucleus when neutrons are at the inner shells they don't decay "  is  true when (beta-unstable) nuclei are still relatively close to the beta- stability line. But the main criteria for beta-decay is always the same: positive decay Q value. Thus, a decay condition is defined by the relative energies of the combined neutron and proton quasi-particles. How different are the main oscillator numbers of the shells in which they are sitting  depends, of course on N/Z ratio. In the most neutron-rich  region of nuclear chart near the 78Ni, the decays from the completely filled neutron shell are experimentally known. Example:  Ga isotopes with N>50 ( their  half-lives measured up to N=55. Physical Review Letters, 2012, v. 109, 112501. ). One can find there both the  Gamow-Teller decays from filled N=50 shell and first-forbidden decays from partially filled N=56 sub-shell. They give a competing contributions to the total half-lives. Also the delayed one-neutron and even two-neutron  emission is possible in these nuclei. That is it about the beta-decay of the neutrons inside the nucleus.  What Shad B. mentioned is for the direct particle-decay channel. For that we have to go to the neutron drip-line nuclei. Still in these hypothetical species we will also find the beta-decay from the filled N-shells. Look e.g to doubly-magic 176Sn which seems to be  particle-bound system (at least in some versions of energy-density functionals).

I believe that a further clarification may help this discussion. The question by Churamani involves the decay of a neutron inside a nucleus. When permitted, under the conditions outlined by Ivan Nick B., the process occurs spontaneously starting from the bound, though beta-unstable, ground state.

The spontaneous emission of a neutron by a nucleus, where there, if this is the case mentioned by Shady B., might well be permitted, provided, however, that the ground state, if we can still call it so, is unbound.