The correct statement about stable isotopes is:
A stable nucleus has a similar number of protons and neutrons.
This is true because stable isotopes generally have a balanced ratio of protons to neutrons. While some isotopes can have more neutrons than protons and still be stable, it is not universally true that those with more neutrons are always stable. Many isotopes are stable, and only some isotopes are radioactive.
The other statements in the responses are incorrect. Isotopes can be either stable or unstable, and many of them occur naturally and are indeed stable.