The stars in the galaxy do indeed get thinner and thinner, and there are many stars out there that only a Carrier can now reach, but there is also a hard "edge" to the galaxy, the box within which the entire game universe sits. You can find this box, simply by zooming out in the galaxy map and trying to scroll in one direction forever. It doesn't matter which direction you pick, you eventually hit a point where the scrolling stops - that's the wall of the box. The four "cardinal points" of the galaxy - the points furthest North, South East and West from the Galactic Core - sit several thousand LYs away from the edges of the box, beyond which there can be no stars. But the Stellar Forge algorithm makes sure that the actual stars of the galaxy end well before the wall is hit.
For example: before Carriers arrived, the furthest charted from Sol was the Oevasy SG-Y d0 system, also known as "Semotus Beacon" or "Ishum's Reach". Now that carriers have arrived, the farthest charted star from Sol is still Oevasy SG-Y d0 - there simply are no stars further out then that, even though the actual Northern edge of the box is at co-ordinate x=75895, a good 10,000 LY or so to the North of Oevasy SG-Y d0.
The box isn't a cube, it's quite flat, because the galaxy is flat. The Upper lid of the box is at y=9015, and the Lower base is at y=-10985, so it's "only" 20kLY thick. There are actually a few hand-placed stars that have been given co-ordinates outside the box - notably, a cluster of pulsars that are far Below the galactic plane. However, the game gets confused when you try to actually select these stars, because they're outside the box. Just type "PSR" into the galaxy map search bar, and watch it try to zoom Down to a cluster of pulsars somewhere in the y=-11200s, before snapping back to empty space at y=-10985.
So, we can dream/fantasize about jumping all the way to another galaxy if we want... but FD will have to make us a bigger box first.
