Learn Croatian: Ogrlica koju su ukrali je vrijedna. - The necklace which they stole is valuable.

The relative pronoun must match the noun it describes (ogrlica, which is feminine singular) but it takes the case of its role in its own clause. Here, the necklace is the direct object being stolen, so we use the feminine accusative form, koju.

The current lesson is about animate vs inanimate nouns in the accusative. Does that rule apply to koju here?

No. The animate versus inanimate rule in the accusative case only applies to masculine singular nouns and pronouns. Because ogrlica is feminine, its accusative pronoun is always koju, regardless of whether the object is a living thing or not.

Why does the auxiliary verb su come right after koju?

su is an enclitic, which is a "weak" word that always wants to be in the second position of its clause. The relative pronoun koju starts the new relative clause ("which they stole"), so su immediately takes the second spot.

Why does the sentence end with the feminine adjective vrijedna?

The adjective vrijedna describes the main subject of the sentence, ogrlica (necklace). Even though an entire relative clause (koju su ukrali) separates them, the adjective still has to match the feminine singular noun it describes.