If it's a sp game, you can probably just have it so once the particle leaves the camera projection area, the particle disappears from existence or something.
Or perhaps have it still exist, but not try to render it, just try to remember it's position incase it hits a ship off screen or something.
As for background stuff, ...stars...does the trick
In all seriousness though, as suggested, planets in the background, also maybe do some space station ruins, or the hulls of empty space ships from a massive battle floating around which would be not only in a background layer, but also a foreground layer to make if feel like the player is flying through the aftermath, rather than past it.
Shooting stars, comets, asteroid fields, nebulae, black holes, anomolies that you can make up yourself to look cool, they don't need any explanation
Random space suit floating around, some kind of space creatures in a swarm like X2 and X3 have space flies (which are illegal, but make lots of money in game)
Just go crazy with ideas, but not to the point where the player is always going to see a bit of everything, make it random enough and frequent enough so that the player will see these things, but not so frequent that the player is going to see it all the time.