I go for option 1.

In all programming languages that I know, integers have a maximum number. E.g., in C that'd be 2,147,483,647. After that, you would run into an overflow, resulting in either...

• a crash (train stops, no more deaths),
• death count suddenly turns negative (all people previously killed are suddenly alive again and even new people are generated out of nowhere) - until we reach the next overflow when people disappear and start dying again
• or - if it's an unsigned integer - death count resets everytime we reach the maximum limit

So compared to option 2, we have a chance of stopping the death count. And even if the train keeps running, we have essentially option 2 but the same people only die very rarely. If we assume a cycle of 1 death per second and an integer boundary of 2,147,483,647, that's just one death every 68 years per person involved. Seems more fair to me compared to 100 people constantly dying over and over again.