Now search all of history, from the time God created people on the earth until now, and search from one end of the heavens to the other. Has anything as great as this ever been seen or heard before?
The boundary of our solar system is the heliosphere's edge. The heliosphere is all that area where the solar wind's outflow tends to predominate over incoming interstellar radiation. There is a loosely defined boundary where the solar winds drop off and cosmic radiation heading toward the solar system begins to predominate. But as you can imagine, this is not a sudden shift. It's not a stable line, either. The intensities of both the solar winds and cosmic radiation vary substantially over time, so it's a constantly shifting zone.
It's somewhat like this with galaxies. In general, we define a galaxy as all that space within which the gravitational pull of the galaxy's center of mass is still strong enough to keep stars in orbit around the galactic core. But this is a highly amorphous line. Its exact location differs by coordinate and is controlled by the mass and center of mass of the galaxy in question as it competes with other large-scale structures nearby. As you can imagine, the mass and coordinate location of the nearby large scale structures is a constantly moving, seething target. So long as there isn't a competing mass overpowering that of the galaxy in question, it would be possible for a star or planetary system -- given the right mass and velocity -- to fall into orbit around a galaxy but be far, far outside that galaxy's main body of orbiting objects.