Whoever had the lice, they're dead now

This sentence is from South Park. There was a lice problem in the school and the children demand that their teacher Mrs. Garrison tell them who exactly had the lice. She says that it's not important because

Whoever had the lice, they're dead now.

Now, obviously she means that the lice are dead, not the person who had them. But doesn't her sentence mean (strictly speaking) that the person is dead? In similar constructions in Standard English, can they refer to the object of the main clause? I see no syntactical difference between the first sentence and the seemingly wrong

Whatever damaged the keys, they're in my pocket now. (= the keys are in my pocket)

I guess my question is

• How should I parse the first sentence?
• Is the second sentence wrong?
• If so, What would be the difference between the first and the second sentence that makes the first sentence OK, but not the second?

Hope the question is on topic.

_{I am having some difficulty properly tagging the question. Please help :)}

I think you've answered your own question. This is a pun of sorts, one might even catagorize it as a paraprosdokian.

But doesn't her sentence mean (strictly speaking) that the person is dead?

You're exactly right! In fact, I think that's what we're all supposed to think when we first hear the sentence, before we realize it's the lice that are dead.

The way the sentence is constructed invokes images of a dramatic line in a movie, something along the lines of, “Whoever it was who just tried to save the world, he's dead now.”

This is classic adult animation humor, where the scriptwriters rely on clever wordplay to invoke a laugh from an adult audience.

You've hit upon a key problem in natural language processing. Spoken language is full of ambiguity without context. In the case of the "whatever," however, I'm not seeing how "they're" could refer to "whatever."

Dangling pronoun.

• Rather than parse it, you should burn it, and recast. Unless the joke is the ambiguity, or an example of ambiguity. "Whoever had the lice, the pests are dead now." or "Whoever had the lice, that person is dead now," depending on which meaning to resurrect.

• The second sentence is not wrong because of a dangling pronoun, as @ErikReppen points out. This is because the plural pronoun they could only apply to the plural object keys and not to the singular object whatever. It doesn't even trip on the use of they as a genderless pronoun for people, as @TimLymington noticed. However it is jarring because the subject is the extra-vague whatever, and this steers the reader into thinking that what follows the comma will elaborate on the subject, versus the more specific object keys. Less jarring: "I don't know how the keys were damaged, but I have them in my pocket now."

• First sentence, dangling pronoun, technically ambiguous as to who died, possibly intentional given the dark dark minds who created it. Second sentence, misleading by emphasis as to where the meaning is going.