Learn Italian: Il paziente non sapeva che quella donna fosse la propria moglie. - The patient didn't know that that woman was his own wife.

You are right that affirmative statements of knowledge take the indicative because they express certainty. However, this sentence uses non sapeva (didn't know). Negative declarations of knowledge introduce doubt or a subjective view of reality, which triggers the subjunctive in Italian.

Why do we need the imperfect subjunctive fosse here instead of the present subjunctive sia?

This is due to the sequence of tenses. The main verb non sapeva is in the past (the imperfect tense). To show that her being his wife was a fact at that exact same time in the past, the dependent clause must use the imperfect subjunctive.

Does the use of the past tense fosse imply that the woman is no longer his wife?

Not at all! The imperfect subjunctive fosse simply aligns the timeline with the past tense main verb. It describes a state of being that was true at that moment in the past, regardless of whether she is still his wife today.

Why use propria instead of sua for his?

Proprio (and its feminine form propria) is a possessive adjective meaning one's own. It is often used instead of suo or sua when the possessor is the subject of the sentence (here, il paziente). It adds emphasis and completely eliminates any ambiguity about whose wife she is.