another way to tackle this problem is to make a grid of background sprites, and rotate them so that there is always one ready to scroll on to the screen...
I made a sample to show you what I mean. The screen is 1920 x 1080, so I made a grid of 9 background sprites (3 rows of 3 sprites - each 1920 x 1080). You start in the middle one. Which ever way you move, whenever you move into a new row or column of the grid, the row or column furthest away gets moved up to the front in the direction you are moving. This keeps you in the middle of the grid, so you can move in any direction and there is a sprite up ahead to scroll on.
to make it easier to see it in action, you can press Z to zoom out, and press C to change the backgound sprites to solid colors. Zoomed out you can see the row or column get rotated to the front.
(Press Z again to zoom back in, and press S to show stars again).
It uses Unbounded scrolling, so you can fly in any direction forever - the backgounds keep rotating under you so you always see stars (or the solid colors).
The only thing interesting that I put in the universe is at sector 0,0 and 3,3
(you start in 1,1).
use the arrow keys to move the spaceship, spacebar to fire - but there is nothing to shoot.