^ Kobayashi Maru. You've put together a pretty wild and wacky rare scenario there.
The needs of the many outweigh the needs of the few, or the one.
In Stargate Universe, a dying Senator sacrificed his life to save the others, by manually activating the closure of the shuttle doors from inside (it couldn't be done from the outside). If nobody had done this, everyone would have died with the entire ship's atmosphere vented.
Eleen is stuck in the only way out, oxygen is going, and everybody in the tunnel is going to die unless she gets unstuck. The right thing would be to clearly state the facts and ask her kindly to sacrifice herself. She'd be dying anyway, what with massive internal injuries. If she was an upstanding person, she'd say "shoot me". And, the captain would have to do it. If she declined, and remained selfish to not only die but take a few other people with her, the proper thing would be to knock her unconscious, then use the phaser to widen the hole (and kill her).