The Earth will soon be a dead planet. The oceans will freeze solid. The atmosphere will turn into liquid air rain. Some deep bunkers may be able to prepare for the catastrophe, but the limited time to prepare will mean that long-term even these bunkers will will succumb to the deep freeze.
If the dust period is short enough, some bunkers could conceivably survive long enough, but pretty much all infrastructure on the surface will be severely damaged if not outright destroyed.
I doubt we could make a workable replacement biosphere in the short time to prepare. Noah's ark was simple compared to the task facing the survival of the earth in 2015.
The 100% drop in solar that comes in 1 year, at the point the only heat source left will be thermal flow from the core of the earth which is about 4000 times less than solar flux. I am assuming that the earth is still a black body radiator and the only significant heat source left on the planet is heat flow from the interior. This is over 4000 times less than the solar heating.
A quick quick for black body temperature shows the earth will be about 35 degrees Kelvin at equilibrium so the final temperature is clearly cold enough to freeze solid virtually all of the atmosphere.
Currently mankind generates about one-third as much energy globally as comes from the interior, but as mankind dies off this necessarily goes to zero.
Mankind 15 TW, geothermal 47 TW, Solar 173,000 TW
Upon further reflection, a different set of assumptions leads to a completely different outcome. If the dust absorbs 100% of the sun and it completely encloses the sun, it will receive the entire output of the sun and re-radiate the energy as thermal radiation. For dust at equilibrium at the sun's surface the dust equilibrium temperature will be 6000K just like the sun's surface.
As you move away from the sun the equilibrium temperature of the dust will necessarily drop. Ignoring convection, the equilibrium temperature at the distance of 1 AU would be about 255 Kelvin. The earth would eventually reach a temperature somewhat above 255 K due to it own greenhouse effect -- since the frequency mix would be completely different, I won't guess what the final temperature would be.
As the incoming flux would be nearly uniform from directions, there would be no temperature differences between the equator and the poles or seasonal variations either.
All surface plant and animal life still die out because plant photosynthesis requires the high energy photons of the sun, not the infrared that would come from the dust.
Transitory effects could still be quite severe. But at least there would be some hope of a possibly survivable outcome for some small population.