Since the sun orbits around the center of mass of the solar system would it be possible for you to be 'trapped' in that region of space or would the suns gravity just pull you in?

I'm just kind of confused by this, the center of mass of the solar system can sometimes be entirely outside the sun so the sun will be orbiting a point that is essentially empty, if gravity is making the sun orbit that empty point along with all the other planets would that mean if you sent an astronaut to be in that specific point he would merely orbit that point instead of the sun or will the suns gravity just pull him in?