For candy clothes to work they've gotta be little rings like micro-chainmail or something, as Putnam said, it's utterly stiff. It's even stiffer than Xeelee Construction Material, which is another absurdly sharp/ridiculously tough/unusually light material but with a bit better handwaving and physical property considerations.
If it is just a high rounding error and it is merely pushing into the speed of sound ~= speed of light area then you've still got other problems to think about.
The maximum edge is 100,000 as I recall, obsidian has a max edge of 20,000 which we can go ahead and call a monomolecular edge, these are real things, and they are brittle as you would expect.
With a properly calibrated microtome you can slice molecule thick sheets off of a sample using glass blades.
Now we want something 5 times as sharp and literally unbreakable?
Going back to the Xeelee Construction Material, it was "a proton-width thick" (the handwaving was that it is what you get if you were able to violate the Pauli Exclusion Principle so quarks could share ground states, releasing a shit-ton of binding energy, and no longer spread in probabilistic clouds) and "stronger than life itself", Sufficiently Advanced Technology and all that jazz.
A sharp piece of candy might be able to cut a piece of XCM, in one of the first stories where the stuff was detailed it was used to surf the blast wave from a nova explosion. The times pieces of it get damaged are when you start throwing around buzzwords like "gravity wave laser" or "monopole cannon" or "ultrarelativistic neutron star impact"... and candy might be tougher.
It is so far beyond the common monofilament fiber tropes as to make them look like a soggy noodle by comparison.