Learn Italian: Ero stordito e non sapevo che quella benda fosse sulla mia testa. - I was groggy and didn't know that that bandage was on my head.

The phrase non sapevo che (I didn't know that) is a negative declaration of knowledge. While stating what you do know takes the indicative, stating what you do not know introduces doubt and subjectivity, which triggers the subjunctive. Because the main verb sapevo is in the past, we use the imperfect subjunctive fosse to show both things were happening at the same time.

If the speaker actually knew the bandage was there, would we still use fosse?

No. Positive statements of knowledge express certainty and require the indicative mood. If the sentence were positive, it would be Sapevo che quella benda era sulla mia testa, using the imperfect indicative era.

Why do we use the possessive in sulla mia testa? Aren't you supposed to drop possessives with body parts in Italian?

Italian usually avoids possessives with body parts when an action is being done to the subject, often using reflexive pronouns instead (like mi fa male la testa). However, when simply describing the physical location of an external object on a body part, using the possessive with the definite article (la mia testa) is normal and adds descriptive clarity.

How would the sentence change if the speaker were female?