Based on both common and uncommon nuzlocke rules you can do one of the following:
1) game over (based on rule of if you white out, you lose)
2) second life (based on rule of having Pokemon in the pc counts as a second life)
3) one chance continue encounter (based on a less common rule that if you white out with no Pokemon in the pc, you have one chance to catch a new Pokemon in an area you've already been too, in order to continue the run, but if you fail the capture, it's game over.)