First I have to warn everyone that is about scientific articles and not everyone likes this stuff. Moreover is not approved fact.
Nothing conclusive but below some studies about unconjugated hyperbilirubinemia (like in Gilbert's Syndrome) and some possible protective role for liver. But keep in mind that this is not about situation when high bilirubin level is because of liver damage (and is a sign of bad synthetic function) from my understanding.
GILBERT'S SYNDROME AND NASH: A PROTECTIVE EFFECT OF UNCONJUGATED HYPERBILIRUBINEMIA
"Conclusion: This study shows significantly lower prevalence of unconjugated hyperbilirubinemia in patients with histopathologic evidence of steatohepatitis (NASH) compared to simple steatosis and a normal control group. It is possible that sustained unconjugated hyperbilirubinemia inhibits oxidative stress, inflammation, and hepatic fibrogenesis, preventing NASH. This may have significant therapeutic implications for patients at high risk of developing NASH with medications which elevate unconjugated bilirubin such as probenecid, rifampin, phycobilins, and algal biliverdin metabolites."
livertree.easl.eu/easl/2012...
And also:
" Association between bilirubin and risk of Non-Alcoholic Fatty Liver Disease based on a prospective cohort study"
"Thus, it can be conceivably speculated that bilirubin could be linked to decreased risk of NAFLD, a hepatic manifestation of metabolic syndrome, probably induced by inhibiting oxidative stress."
"Elevated serum bilirubin levels are inversely associated with nonalcoholic fatty liver disease"
" In conclusion, this study, conducted with a large number of healthy populations, confirmed the inverse relationship between serum bilirubin level and the occurrence of NAFLD. Based on this result, further clinical studies on the disease prevention and treatment by controlling serum bilirubin level will be required in the future.
ncbi.nlm.nih.gov/pmc/articl...
On the other hand no correlation was found here (Chinese population) :
"Genetically Regulated Bilirubin and Risk of Non-alcoholic Fatty Liver Disease: A Mendelian Randomization Study"
"Based on a Mendelian randomization approach, our data suggest that increased bilirubin levels is unlikely a causal factor for a reduced risk of NAFLD."