Learn Danish: VIP-kunden blev lovet særbehandlingen. - The VIP customer was promised the special treatment.

This showcases the lesson's focus: promoting the indirect object. In the active version of this sentence (like 'They promised the VIP customer the special treatment'), VIP-kunden is the indirect object. Just like in English, Danish allows this indirect object to become the subject of a passive sentence.

What is the grammatical role of særbehandlingen here, since the sentence is passive?

It acts as a retained object. Even though the sentence is passive and the original indirect object became the subject, the original direct object (særbehandlingen) simply stays in place as the object of the verb blev lovet.

Could we use the s-passive (lovedes) instead of blev lovet for this sentence?

You could, but blev lovet sounds much more natural for this specific scenario. The Danish s-passive is generally preferred for general rules, ongoing states, or instructions. Because this sentence describes a specific, isolated event in the past, the blive-passive is the standard choice.

How does the word særbehandlingen break down?

It is a compound of the prefix sær- (special or particular) and the noun behandling (treatment), plus the definite suffix -en. You will see sær- in many other useful Danish compounds, such as særtilfælde (special case) and særregel (special rule).