individual-level random effects and the idiosyncratic error

#1
Can anyone explain how some of the explanatory variables could be correlated with individual-level random effects, but that none of the explanatory variables are correlated with the idiosyncratic error? How does that work? Could someone please provide an example?

"The estimators implemented in xtivreg assume that a subset of the explanatory variables in the model are correlated with the idiosyncratic error . In contrast, the Hausman–Taylor and Amemiya–MaCurdy estimators that are implemented in xthtaylor assume that some of the explanatory variables are correlated with the individual-level random effects, but that none of the explanatory variables are correlated with the idiosyncratic error."