On the one hand, the possibility exists that the buck gets passed forever, especially as the kill count numbers grow substantially making the impermissibility of allowing the deaths grow with it. It's not likely the any given person would kill one stranger, let alone millions.

On the other hand, in an infinite series, even something with miniscule odds will still eventually inevitably happen, and some psycho will instantly become the most infamous murderer in history, followed immediately by the person that didn't just kill one person and end the growth before it started.