First, I've never seen a close to zero real LDLc, except for a few cases of hypobetalipoproteinemia severe homozygous, with values between 5 and 10 mg / dl LDL-C and with serious health problems, partly due to lack of soluble vitamins, and in any case these figures never suddenly appeared .
However, it is possible to see figures LDLc near zero or even negative if used indiscriminately the Friedewald formula (which for me is not valid if triglycerides are above 200 mg / dl) and appears suddenly with an isolated hypertriglyceridemia (like a hyperchylomicronemia): but it is not a real situation but an artifact. I do not know if the situation you mention is possible, but I would be even surprising even in cases of very severe decrease in hepatic protein synthesis.
In addition to the above answer of lab artifact or error, a sudden decrease may be due to a reaction in the blood which precipitates the LDLc with WBC’s and therefore, it would still be artificially low due to bound LDLc in vivo.
I never found a Zero concentration of LDL-Cholesterol, but it is very low in rare patients with a-betalipoproteinemia. Electrophoresis of plasma in agarose gel must be run in those cases, to see the origin for chylomicrons, beta for LDL and pre-beta region for VLDL, respectively.
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