Solar system position is changing all the time, at over a million miles per hour. It is traveling around the edge of the Milky Way galaxy every 220 million years. A long trip over a great distance of over 300,000 light years. We can see over centuries that the nearby stars, some of which travel with our sun, don't move much. But some don't travel with our sun. Their positions change. In a far future, many of the constellations we know today will not be the same shapes. The Big Dipper is one example. Only some of its stars go in the same direction.
If you mean the solar system being closer or farther from the center of the galaxy, or not in it at all, that will happen in a few billion years. Our galaxy will collide with M31 in Andromeda, another giant spiral. The shapes of both will distort and rearrange. Our sun will be in a very different position compared to now. Which one and how much change, no one can be sure now, and probably there will be no humans around then to see and measure.