Learn Finnish: Laiton kamera salakuljetetaan tehtaaseen. - An illegal camera is smuggled into the factory.

This perfectly demonstrates the passive object rule. When a complete object is acted upon by a passive verb like salakuljetetaan, it takes the nominative case (its basic dictionary form). It drops the usual -n accusative ending it would have if an active subject were doing the action.

Would the case of the object change if someone specific was doing the smuggling?

Yes! If this sentence had an active subject, such as 'The man smuggles an illegal camera', the object would take the normal genitive-looking accusative case ending -n (laittoman kameran). The object case 'drops' to the nominative here only because the verb is passive.

How does the word salakuljetetaan mean 'is smuggled'?

This is a compound verb in the present passive. It combines sala- (related to salaa, meaning 'secretly') and kuljettaa (to transport or carry). The -taan ending makes it passive, so literally it translates to 'is secretly transported'.

How does the dictionary form tehdas (factory) change into tehtaaseen?

Tehdas belongs to the -as word type. To find its stem, the -as changes to -aa-, and it undergoes consonant gradation from the weak hd to the strong ht, resulting in the stem tehtaa-. Because this stem ends in a long vowel, the illative 'into' ending becomes -seen.