If we state that some professors in one political science department are racist, we can't suddenly conclude that all of them are. If any term is undistributed in its premise but distributed in the conclusion, then we have the fallacy of illicit process. Such a syllogism is invalid. There may be only one negative premise and if there is, the conclusion must be negative. If both premises are affirmative, then the conclusion must be affirmative .
Negative statements exclude classes from each other.
No elephants are birds. No refrigerators are birds. If we have two such negative premises, then we have no linkages to the Middle term except this exclusion. If we have one negative premise and one affirmative premise, then it's possible to have a valid conclusion, but it must be negative since it will inevitably express exclusion. No elephants are birds.