Apparently not as distinct entities. One way to look at this is that nuclei are 'bags' of quarks which may spend part of their time bound in triplets as protons and neutrons, and the other part of their time as a broth of quarks interacting via gluons with all other quarks in the bag. If you were to probe this bag by scattering low energy particles off of it, the bag would look like a collection of distinct protons and neutrons, but at higher energies, the distinctions between individual protons and neutrons begins to weaken .At least that's the way I like to think about the situation.
When fission occurs, the fission products are not present within the parent nucleus as tagable protons and neutrons. The fission process itself is a quantum mechanical tunneling process in which one or more nuclear particles tunnel out of the collective potential of the nucleus and become free particles. It is not possible to know a priori which particles will tunnel out of the nucleus, any more than it is possible to know which particular collections of individual protons and neutrons will emerge as the product nuclides of the fission process. All that one knows is that certain nuclei favor tunneling ( fission) events that involve certain fixed combinations of protons and neutrons. These fission products, however, are only assembled at the instant of the tunneling/fission event. So far as I understand the process, they do not pre-exist within the parent nucleus.