Even yet another Borg question, Part VII

Assuming the Federation and Species 8472 were to leave the Borg alone (or at least, not be able to kill them anymore), what would be their ultimate goal? If they assimilated everyone in the galaxy, would they head off to other galaxies?

I imagine that they’d probably run into trouble from the Dominion, Romulans, or Klingons… but if we assume that the Borg were allowed to progress unimpeded, well…

Personally, I think they’d probably just assimilate the galaxy, and then eventually die out from lack of innovation. By the end of Voyager, they were portrayed as completely unable to come up with new thoughts, and were also unable to reproduce without assimilating other species. They’d stagnate themselves to death.