It's worth noting that they don't always assimilate entire species.
The best example of this is Guinan's race, the El-Aurians. The Borg assimilated their world(s), and effectively shattered their species's civilization, but there are still El-Aurians in the universe. They seem to have been reduced to individuals roaming the galaxy in solitude, but I can't remember any mention of the Borg "hunting down" the last survivors. It would seem that the Borg won the battle, took what they wanted, and didn't care about the stragglers.
Similarly, the Borg tried twice to assimilate the Federation (at the Battle of Wolf-359 and again at the Battle of Sector 001), but seem to have put little further effort into the endeavor. Two cubes destroyed in the pursuit of assimilating a distant civilization, (and Q makes it clear in "Q Who?" that Federation tech isn't terribly impressive or attractive to the Borg), and it seems to have become more trouble than it's worth.
And, while its canon status seems somewhat debatable, the Borg even seem to have scooped up a few Romulan colonies before (apparently) deciding that Romulan tech wasn't worth even a first assault.
When the Borg decide that your technology or culture is worth assimilating, they come at you hard and they take everything. But if you don't have anything they want, or if they've taken everything from you and turned you into space-gypsies, they don't seem to care what happens to you.