You've all heard Jimmy Dean's ol' country classic, Big Bad John. For those who don't remember the lyrics, Big Bad John is a loner. No friends, no family. Works in a coal mine but doesn't make friends with his co-workers.
Cave-in occurs. Big Bad John is the only guy who can hold the roof up long enough for the others to escape.
Big Bad John can't hold it up long enough for the others to escape, get help & equipment & come back to save him.
Whatever happens next, Big Bad John dies.
There is no one in his life who will benefit from his death (the escaping miners don't benefit by his dying, only by his holding the roof up long enough to get away, and they do make an effort to come back to save him but John can't hold out long enough).
Now, from an Objectivist POV, was Big Bad John morally / ethically correct to sacrifice himself so that others might live?
He can not benefit from his sacrifice, not even so much as seeing his family gets money for his death.
He has nothing, he owes nothing, he is completely 100% free and autonomous.
Based on Ayn Rand's philosophy, why in the world would he sacrifice himself to save others?