Question

Does the stability of protons and neutrons in the nucleus depend on the electrons ?

Answer 1

No, the electrons do not affect the stability on the nucleus.
Both protons and neutrons are in same place (the nucleus). Electrons are not in the nucleus.
The stability of the nucleus depends instead on the relative numbers of protons and neutrons.
if there are too many or too few neutrons for a given number of protons, or if the nucleus is just too big,the nucleus becomes unstable.

Answer 2

No, because electrons do not reside in the nucleus. But if you are wonder if the Number of electrons and protons effect the atom then yes, it does. You must have a equal number of electrons and protons but as for the stability of the atom, electrons won't mess the nucleus up.