Is it possible for a binary classifier to have a recall of
0.0 for one of the classes and
at the same time an area under the ROC curve (AUC) of
1.0 for the same class?
ROC curves are false negative rate vs true positive rate graph. If you have AUC = 1, by definition you have perfect classifier.
From Information retrieval viewpoint ; if you have AUC = 1 then you have perfect recall and perfect precision. You recall all documents which exists about this topic, also all the documents you recall are relevant to your topic.