If the Sun moves into 4th Density, will it then leave 3rd Density? Yes. Those portions of the Sun which are inert, used up so to speak, will remain as a gravitational center for the 3rd Density planets orbiting the Sun, including the 12th Planet which is not scheduled to become a 4th Density planet in step with the Earth. With less of a gravitational pull, the 3rd Density planets in your Solar System will move outward, assuming a larger orbit. Life remaining on the surface of the 3rd Density Earth will freeze to death as the surface of the Earth cools under the diminishing rays from a dimming 3rd Density Sun. We will leave some undesirables behind - mosquitoes, for instance, which serve no biological purpose except to feed themselves and support the transport of parasites and disease, and tapeworms, who likewise are not a necessary link in any symbiotic cycle. The agents of many diseases such as a virus, bacteria, fungus, or invading parasite will not be moved during the shift. All these will freeze to death.
Ultimately, even the core of the Earth will cool, the lava hardened, but life underground will continue for some Millennia before the heat at the center of your old home begins to fade. The Men In Black and others coexisting with you now, in underground homes, are not scheduled to move to 4th Density in step with humans living on the surface. The Men In Black and other underground inhabitants will live, for some Millennia, with the impression that your Sun died. Suns do die quickly, and not all have that last glorious burst of life, the Super Nova. Most do not. During the transition to 4th Density there will be enough fuel left in the 3rd Density Sun to give an orderly death. Those on the 12th Planet, looking through their telescopes, will see a fading Sun, not one that winked out suddenly. They will assume that the Earth's Moon was torn away during their passage through the solar system, not unexpected as in truth this is how the Moon was placed as a satellite of the Earth in the first place.