In Lingua Latina Per Se Illustrata, chapter 6, exercise 5.8, I see the sentence:
Dominus verberat servōs ____ nōn pārent.
Since servōs is accusative, I put quōs in the blank. But the answer key says quī is the correct answer. Why?
The case of a relative pronoun indicates its role inside the subordinate clause, not the main clause.
Since the servōs in the main clause are the subject of pārent in the subordinate clause, a nominative relative pronoun is needed: quī.
If that seems strange, here are three considerations that can help make it seem normal:
1. It works the same way in English, although our last pronoun that works this way is fading:
The cat killed the rat who ate the corn.
The cat killed the rat whom fate had chosen.
2. Making the relative pronoun match the case in the main clause would lose information and really wouldn't make sense in practice. The relative pronoun tells you that the same noun plays a role in two clauses: the main one and the subordinate one. You already know the noun's role in the main clause, because that's indicated by its case in the main clause. The only word available to indicate the noun's role in the subordinate clause is the relative pronoun, so it wouldn't make sense to make the relative pronoun duplicate the antecedent's case in the main clause.
3. Ultimately, only exposure and practice can really convince your brain that this is normal. So, here are some of the sentences from the chapter that illustrate the principle:
Servī quī lectīcam portant fessī sunt.
Saccī quī ā Syrō et Lēandrō portāntur magnī sunt, sed saccus quem Syrus portat nōn tam magnus est quam saccus quī ā Lēandrō portātur.
Is quī viā Latīnā venit per portam Capēnam Rōmam intrat.
And here's Ørberg's terse explanation in the margin:
saccī quī ā Syrō et Lēandrō portantur = saccī quōs Syrus et Lēander portant
Relative pronouns (like quis/quis/quid) don't agree with their antecedents for case; instead, it gets that from its position in the subordinate clause. Note that they still agree in gender and number, since it's supposed to be a stand-in for the noun.
Because the pronoun stands in for a nominative use, the subject of the clause -- i.e. "servi non parent" -- it has to be nominative, which means it's "qui". Because "servos" is plural and masculine, the pronoun does as well.
You can find out more about relative pronouns here.