This is a bit old question I had missed so my answer will be short, just some references.
The stringy predictions are, of course, extracted from the AdS/CFT correspondence. It's my belief that a reader should first be familiar with the existence of the AdS/CFT correspondence due to Maldacena because the third law is just a very tiny story inside the AdS/CFT.
AdS/CFT says that physics of 4-dimensional theories of various kinds - not only gauge theories - is equivalent to (quantum) gravitational i.e. stringy physics in a higher-dimensional spacetime, five-dimensional anti de Sitter space. Various analyses of fluids and plasmas etc. without gravity may be typically translated to analyses of black holes in a higher-dimensional spacetime. I can't review the AdS/CFT here; typical reviews have hundreds of pages.
Now, the $T=0$ limit of the boundary matter - "crystal" - are typically mapped to the extremal limit of a black hole. The third law, i.e. $S\to 0$, holds because this extremal limit is simultaneously singular. The area goes to $A=0$ in the limit of low temperatures which translate to some limit of the black hole parameters.
Nevertheless, there have been arguments that with some particular bulk theories, the extremal limit may be a non-singular black hole with a nonzero area, and therefore nonzero entropy. See e.g.
Let me just mention that papers just a few months older were claiming that they had various proofs that the third law had to hold, e.g.
At any rate, for these exotic enough theories, one can't really say how the hypothetical material violating the third law looks like. The AdS/CFT surely doesn't construct molecules out of the usual atoms. It just says that if the description of the dual theory has a particular form, we may expect violations of the third law.
I think that all these people believe that when things are computed accurately enough to discuss the real material, the third law will always hold. In limited contexts, it can be proved, in broader contexts, it seems to have a loophole. At any rate, the discussion of the third law may be performed from a completely different angle if we borrow AdS/CFT.