Alternate realities, time travel, holographic recreation, or Kobali-fication are all possibilities.
I can see the parallels version of VOY now:
KIM: The rate of quantum incursions is increasing exponentially. At this rate, the sector will be completely filled with Voyagers within three days.
TOM : Captain, we're receiving two hundred eighty five thousand hails. About 280,000 from an Ensign Kim, 5 from a Lt. Kim, 3,000 from a Lt. Byrd, and the others seem to come from assimilated Voyagers telling us we will be assimilated. Most of the Voyagers seem to be much worse off than we are anyway and most seem to operate on a skeleton crew.
Captain <looking grey and nauseous > did you just say Lieutenant Kim?