Learn Finnish: Aavekaupungissa kummittelee, mutta en pelkää kenenkään varjoa. - It's haunted in the ghost town, but I'm not afraid of anyone's shadow.

This is the genitive (possessive) form of the negative pronoun kukaan (anyone / no one). When inflecting words like kukaan or mikään, the case ending is inserted between the base word and the -kaan/-kään suffix. The genitive stem of kuka is kene-, so we add the genitive -n, and then the clitic -kään. This gives us kene- + -n + -kään = kenenkään (anyone's).

If the object of the sentence is "anyone's shadow", why is varjoa in the partitive instead of the genitive?

There are two reasons. First, the verb pelätä (to fear) is a partitive verb, meaning its object must always be in the partitive case (varjoa). Second, negative sentences (like en pelkää) force the object into the partitive anyway. The pronoun kenenkään remains in the genitive because it tells us whose shadow it is, but the shadow itself is the grammatical object.

Why is there no word for "it" before kummittelee (it is haunted)?

Finnish frequently uses a subjectless 3rd-person singular verb to describe a general atmosphere, condition, or the weather. Just like sataa means "it is raining", kummittelee alone means "it is haunted" or "there is haunting going on". Adding a pronoun like se (it) would sound unnatural in this structure.