This question is prompted from the scene in the film First Contact, when the Borg are outside the Enterprise creating the transmitter to communicate with the Borg of that time period, on the main deflector dish, they are working on that transmitter for some time, at least a few hours, yet they have no air and no protection for their biological cells to the extremes of space.
How did they survive? Borg are obviously very adaptable to many situations and environments, but they are part biological, and as such that biological part of them still needs the basics for survival: warmth (not the freezing cold that is the vacuum of space) and presumably some kind of atmosphere (be that nitrogen/oxygen or whatever), not the vacuum of space.
The nanotechnology could repair any damage I'm sure, but could it continually repair such extremes of damage such that Borg could survive for extended periods of time outside of a starship?