John being late is a bit inconvenient.
John's being late is a bit inconvenient.
Both of these sentences are correct. It's a bit easier to show what happens in sentences like this if we use pronouns:
- Him being late really annoys me
- His being late really annoys me.
Gerund-participle clauses like this are non-finite. This means that we can't use them as a sentence on their own:
Non-finite clauses in English don't usually use subject pronouns (nominative pronouns) like I, she or he for example. With gerund-particilple clauses, accusative pronouns (me, you, him ... ) and genitive, possessive pronouns (my, her, his ... ) are fine:
- *I don't like he being late. (wrong)
- I don't like him being late.
- I don't like his being late.
Other nouns like John or people don't have nominative or accusative case, so we can use them as subjects without changing them:
- I don't like John being late.
- I don't like people being late.
But these other nouns do have a genitive form John's and people's. Like we did with the pronouns we can use genitive nouns as subjects in gerund-participial clauses like this:
- I don't like John's being late.
- I don't like people's being late. (see note below)
The first example there with John's is perfectly normal. The second example with people's is a bit strange. It's not ungrammatical - it just feels odd. It feels awkward. The Cambridge Grammar of the English Language explains that genitive subjects like this are usually singular, and are also usually short (2002; p. 1192). If the subject is plural, or if it is several words, we prefer not to use the genitive at all:
- I don't like my father-in-law's new wife's being late. (awkward)
- I don't like women's being given worse pay than men. (very awkward)
So, to answer the Original Poster's question, all four of the original examples are grammatical. However, People's killing animals is a bit strange, and speakers don't usually use plural genitive nouns as Subjects.
Hope this helps!
Plural genitive nouns are perfectly fine in most situations. Subjects of gerund participle clauses are unusual because we don't usually use plural genitives here.
The Cambridge Grammar of the English Language Huddleston & Pullum, 2002 (p. 1192-3)