The class of examples I can think of is quite contrived, and relies on two facts:

• possessive 's can mark entire noun phrases (like Jim and Carrie's = [Jim and Carrie]'s, or John's brother's = [[[[John]'s] brother]'s])
• apostrophe-s goes bare, just apostrophe, by convention, when following an S

Going off of the archaism he and his [possessions/progeny], perhaps something like:

That cockroach freaked me out. I hope it and its' deaths are fiery, unpleasant and caused by me.

EDIT: This answer is not valid; see the comment thread.

The class of examples I can think of is quite contrived, and relies on two facts:

• possessive 's can mark entire noun phrases (like Jim and Carrie's = [Jim and Carrie]'s, or John's brother's = [[[[John]'s] brother]'s])
• apostrophe-s goes bare, just apostrophe, by convention, when following an S

Going off of the archaism he and his [possessions/progeny], perhaps something like:

That cockroach freaked me out. I hope it and its' deaths are fiery, unpleasant and caused by me.