I guess you meant that can the nucleus in an atom be in a stable state. Yes, there are four fundamental forces between particles, and the so called strong force is an attractive force that holds all the protons and neutrons together in the nucleus of an atom. This may sound surprising because protons all carry positive charges, so they are supposed to repel each other. But at very small distance, the strong force dominates the repulsive electric force, and the strong force always pulls the protons together.

If you're asking whether we can stabilize the nucleus of an atom, then the answer is...not likely. There are simply too intricate of a balance of forces to strip an atom of all its electrons and then try to stabilize the nucleus artificially.

All atoms contain nuclei. Nearly all elements lighter than bismuth (atomic number 83) have at least one stable isotope, meaning that there is a configuration of protons and neutrons in the nucleus that is stable. The rest of the atom that is not nuclear - the electrons - do not affect the stability of the atomic nucleus.