in a twolevel regression model, how can I compensate for missing values in a level-2 covariate which is only measured at level-2 (varies only between-groups)? FIML only works for dependent variables, correct?
You can mention the variances of the covariates on between. Then they will be treated as dependent variables and distributional assumptions will be made about them but observations with missing on them won't be deleted. You must include all covariates.
It is full-information maximum likelihood - you are just moving the approach up a level, but it's perfectly analogous. I am not aware of papers on it. If you do multiple imputations you would get similar results.