Learn Spanish (Latin America): Fue un rey cuyos descendientes habían perdido el imperio. - He was a king whose descendants had lost the empire.

The word cuyo translates to 'whose', but unlike in English, it must match the gender and number of the thing being possessed, not the owner. Since descendientes (descendants) is masculine and plural, you use cuyos, even though they belong to one singular rey (king).

What tense is habían perdido and how does it work here?

This is the past perfect tense, used to talk about an action that happened before another action in the past. It translates to 'had lost' and is formed using the imperfect tense of the helping verb haber (habían) plus the past participle (perdido).

Could I say era un rey instead of fue un rey?

Yes, era would also be very natural here if you were setting the scene or describing his background. Using fue (the preterite tense) simply treats his reign as a completed, closed chapter in history, which is common when stating historical facts.

Is cuyos descendientes a phrase I should use in everyday conversation?

You will see cuyos constantly in books, news, and formal writing. In casual spoken Spanish, however, it can sound quite formal. While it is grammatically perfect for this sentence and essential to know at a B1 level, native speakers talking to friends might naturally rephrase the sentence to avoid it.